# Project #5345 - precalculus

### pc 4

#1 Points possible: 1. Total attempts: 4
When ${f{{\left({x}\right)}}}=$ $-{{x}}^{{2}}-{6}{x}+{6}$, evaluate the following. Enter your answers as integers or fractions if necessary.

${f{{\left(-{5}\right)}}}=$

${f{{\left({5}\right)}}}=$

#2 Points possible: 1. Total attempts: 4
Given the function ${P}{\left({t}\right)}={2}{{t}}^{{2}}+{7}{t}-{6}$. Calculate the following values:

${P}{\left({0}\right)}=$
${P}{\left({2}\right)}=$
${P}{\left(-{2}\right)}=$

In the 2 boxes below, enter your answer as a simplified expression. Do not use any parentheses. Be sure your variables match those in the question.

${P}{\left({t}+{1}\right)}=$
${P}{\left(-{t}\right)}=$

#3 Points possible: 1. Total attempts: 4
246810125101520-5-10-15-20
Which of the following is the equation of the graph shown?
• ${y}=-{{x}}^{{2}}+{12}{x}-{20}$
• ${y}={{x}}^{{2}}-{12}{x}-{20}$
• ${y}={{x}}^{{2}}+{12}{x}+{20}$
• ${y}=-{{x}}^{{2}}-{12}{x}+{20}$
• ${y}=-{{x}}^{{2}}+{12}{x}-{20}$
• ${y}={{x}}^{{2}}-{12}{x}+{20}$

#4 Points possible: 1. Total attempts: 4
-2-4-6-8-1012345-1-2-3-4-5
Which of the following is the equation of the graph shown?
• ${y}={{x}}^{{2}}-{14}{x}-{45}$
• ${y}=-{{x}}^{{2}}-{14}{x}+{45}$
• ${y}=-{{x}}^{{2}}+{14}{x}-{45}$
• ${y}={{x}}^{{2}}+{14}{x}+{45}$
• ${y}={{x}}^{{2}}+{14}{x}+{45}$
• ${y}=-{{x}}^{{2}}-{14}{x}-{45}$

#5 Points possible: 1. Total attempts: 4
2468105101520-5-10-15-20
Which of the following is the equation of the graph shown?
• ${y}={{x}}^{{2}}-{10}{x}-{9}$
• ${y}={{x}}^{{2}}+{10}{x}+{9}$
• ${y}=-{{x}}^{{2}}+{10}{x}-{9}$
• ${y}=-{{x}}^{{2}}+{10}{x}-{9}$
• ${y}={{x}}^{{2}}-{10}{x}+{9}$
• ${y}=-{{x}}^{{2}}-{10}{x}+{9}$

#6 Points possible: 1. Total attempts: 4
2-2-4-61234567-1-2-3-4-5-6-7
Which of the following is the equation of the graph shown?
• ${y}={2}{{x}}^{{2}}+{5}{x}+{6}$
• ${y}={2}{{x}}^{{2}}+{5}{x}+{6}$
• ${y}=-{2}{{x}}^{{2}}+{5}{x}-{6}$
• ${y}=-{2}{{x}}^{{2}}-{5}{x}-{6}$
• ${y}=-{2}{{x}}^{{2}}-{5}{x}+{6}$
• ${y}={2}{{x}}^{{2}}-{5}{x}-{6}$

#7 Points possible: 1. Total attempts: 4

The above are graphs of quasdratic functions of the form ${f{{\left({x}\right)}}}={a}{{x}}^{{2}}$ , ${g{{\left({x}\right)}}}={b}{{x}}^{{2}}$ , ${h}{\left({x}\right)}={c}{{x}}^{{2}}$${j}{\left({x}\right)}={d}{{x}}^{{2}}$, and ${k}{\left({x}\right)}={e}{{x}}^{{2}}$ where ${a}\lt{b}\lt{c}\lt{d}\lt{e}$. Match each function with a graph above.

•  ${h}{\left({x}\right)}$
•  ${g{{\left({x}\right)}}}$
•  ${f{{\left({x}\right)}}}$
•  ${j}{\left({x}\right)}$
•  ${k}{\left({x}\right)}$

1. purple
2. blue
3. black
4. red
5. green

#8 Points possible: 1. Total attempts: 4
Without using a calculator, sketch a graph of ${f{{\left({x}\right)}}}=-{{\left({x}-{1}\right)}}^{{2}}-{3}$

Clear All Draw:

#9 Points possible: 1. Total attempts: 4
Without using a calculator, sketch a graph of ${f{{\left({x}\right)}}}=-\frac{{1}}{{3}}{{\left({x}+{1}\right)}}^{{2}}+{2}$

Clear All Draw:

#10 Points possible: 1. Total attempts: 4
Consider the parabola given by the equation:
${y}={4}{{x}}^{{2}}+{6}{x}-{5}$

Find the following for this parabola:

A) The vertex = (,
Write your coordinates as numbers or decimals, not fractions.

B) The ${y}$ intercept is the point (0,)

C) Find the two values of ${x}$ that correspond to the ${x}$ intercepts of the parabola and write them as a list, separated by commas:
${x}=$

#11 Points possible: 1. Total attempts: 4
Find b and c so that ${y}=-{12}{{x}}^{{2}}+{b}{x}+{c}$ has vertex ${\left({10},{4}\right)}$

${b}=$

${c}=$

#12 Points possible: 1. Total attempts: 4
A quadratic function has its vertex at the point ${\left({10},-{5}\right)}$. The function passes through the point ${\left({2},{7}\right)}$. When written in vertex form, the function is ${f{{\left({x}\right)}}}={a}{{\left({x}-{h}\right)}}^{{2}}+{k}$, where:

${a}=$

${h}=$

${k}=$     .

#13 Points possible: 1. Total attempts: 4
Write an equation (any form) for the quadratic graphed below

12345-1-2-3-4-512345-1-2-3-4-5

y =

#14 Points possible: 1. Total attempts: 4
${y}={1.2}{{\left({x}-{4}\right)}}^{{2}}+{6}$
is in vertex form.

What is the vertex for the graph of this equation?
vertex:

#15 Points possible: 1. Total attempts: 4
${y}=-{0.4}{{\left({x}+{6}\right)}}^{{2}}-{8}$
is in vertex form.

What is the vertex for the graph of this equation?
vertex:

Which best describes the graph of this equation?
• Parabola opens upward
• Parabola opens downward
• Cannot be determine from information provided.

#16 Points possible: 1. Total attempts: 4
${y}={1.1}{{\left({x}-{40}\right)}}^{{2}}-{20}$
is in vertex form.

What is the vertex for the graph of this equation?
vertex:

Which best describes the vertex for this parabola?
• Vertex is the minimum point on the graph
• Vertex is the maximum point on the graph
• Cannot be determine from information provided.
Will the graph of this equation have any x-intercepts?
• There are no x-intercepts; this graph will NOT intersect the x-axis.
• There is at least one x-intercepts; this graph WILL intersect the x-axis.
• Cannot be determine from information provided.

#17 Points possible: 1. Total attempts: 4
Put the equation ${y}={{x}}^{{2}}+{4}{x}-{5}$ into the form ${y}={{\left({x}+{h}\right)}}^{{2}}+{k}$:

#18 Points possible: 1. Total attempts: 4
Solve the equation : ${\left({x}+{9}\right)}{\left({x}-{6}\right)}=-{44}$

Answer: ${x}=$

Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get ${4}$ and $-\frac{{2}}{{3}}$ as your answers, then enter 4,-2/3 in the box.

#19 Points possible: 1. Total attempts: 4
Find all real solutions of the equation
${3}{{\left({b}+{6}\right)}}^{{2}}-{8}={154}$

After simplifying, the solutions to this equation look like ${b}={A}\pm{B}\sqrt{{{C}}}$ where

${A}=$ ${B}=$ ${C}=$

#20 Points possible: 1. Total attempts: 4
The equation ${4}{{w}}^{{2}}-{3}{w}-{8}={0}$ has solutions of the form

${w}=\frac{{{N}\pm\sqrt{{{D}}}}}{{M}}$

(A) Solve this equation and find the appropriate values of ${N}$,${M}$,and ${D}$. Do not worry about simplifying the $\sqrt{{{D}}}$ portion of the solution.
${N}=$ ${D}=$
${M}=$

(B) Now use a calculator to approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as a list of numbers, separated with commas. Example: 3.25,4.16
${w}=$

#21 Points possible: 1. Total attempts: 4
The graph of ${y}=-{{x}}^{{2}}-{2}{x}+{13}$ is shown below. Use the graph to solve the equation $-{{x}}^{{2}}-{2}{x}+{13}={5}$.

123456-1-2-3-4-5-612345678910111213141516-1-2-3

Enter the solution(s) in the box below. If there is more than 1 solution, separate the values with a comma (example: -3, 2). If there are no solutions, enter DNE for Does Not Exist.

#22 Points possible: 1. Total attempts: 4
The graph of ${h}{\left({x}\right)}=-{{x}}^{{2}}+{4}{x}+{8}$ is shown below. Use the graph to solve the equation ${h}{\left({x}\right)}={12}$.

1234567-1-2-3-4-5-6-71234567891011121314-1-2-3-4-5

Enter the solution(s) in the box below. If there is more than 1 solution, separate the values with a comma (example: -3, 2). If there are no solutions, enter DNE for Does Not Exist.

#23 Points possible: 1. Total attempts: 4
The graph of ${y}={f{{\left({x}\right)}}}$ is shown below. Estimate the solutions to the following. If there is more than one answer, then list the values separated by commas.

1234-1-2-3-41234567891011-1-2-3-4-5-6

Estimate the y-value of the y-intercept

Estimate the x-value(s) of the x-intercept(s). If there is more than one, list them separated by commas.

#24 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123456-1-2-3-4-5-6

What is the domain of this function? (assume there are arrows at the ends of the graph)

Where A =  and B =
What is the range of this function?

Where A =  and B =
On what interval is the function increasing?

Where A =  and B =

#25 Points possible: 1. Total attempts: 4
Find the range of the following function. Express your answer in interval notation.

${f{{\left({x}\right)}}}=-\frac{{1}}{{142}}{{\left({x}-{1180}\right)}}^{{2}}+{1750}$

The range of ${f}$ is

#26 Points possible: 1. Total attempts: 4
ABC Company manufactures picture frames. The weekly profit function is given by ${P}{\left({x}\right)}=-{2}{{x}}^{{2}}+{300}{x}-{920}$

What is the profit/loss when 22 picture frames are manufactured?

Find the quantity that maximizes weekly profit and the maximum weekly profit.

Quantity =

Maximum profit = $#27 Points possible: 1. Total attempts: 4 NASA launches a rocket at ${t}={0}$ seconds. Its height, in meters above sea-level, as a function of time is given by ${h}{\left({t}\right)}=-{4.9}{{t}}^{{2}}+{265}{t}+{374}$ Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level. #28 Points possible: 1. Total attempts: 4 Jesse wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Jesse has 700 feet of fencing, what dimensions would maximize the area of the pen? a) Let ${w}$ be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of ${w}$ Area = b) What width ${w}$ would maximize the area? ${w}$ = #29 Points possible: 1. Total attempts: 4 The cost ${C}$ (in dollars) for a company to produce and sell ${x}$ thousand gadgets is given by ${C}={\frac{{{1}}}{{{30}}}}{{x}}^{{2}}-{2}{x}+{4030}$ (a) What is the company's start-up cost? (b) What is the minimum cost? (c) How many gadgets must the company produce and sell in order to incur the least cost? (Be careful with your units!) gadgets #30 Points possible: 1. Total attempts: 4 A person standing close to the edge on top of a 108-foot building throws a ball vertically upward. The quadratic function ${h}{\left({t}\right)}=-{16}{{t}}^{{2}}+{132}{t}+{108}$ models the ball's height about the ground, ${h}{\left({t}\right)}$, in feet, ${t}$ seconds after it was thrown. a) What is the maximum height of the ball? feet b) How many seconds does it take until the ball hits the ground? seconds #31 Points possible: 1. Total attempts: 4 Suppose the Sunglasses Hut Company has a profit function given by ${P}{\left({q}\right)}=-{0.02}{{q}}^{{2}}+{4}{q}-{20}$, where ${q}$ is the number of thousands of pairs of sunglasses sold and produced, and ${P}{\left({q}\right)}$ is the total profit, in thousands of dollars, from selling and producing ${q}$ pairs of sunglasses. A) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: thousand pairs of sunglasses need to be sold. B) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: thousand dollars of maximum profits can be expected. #32 Points possible: 1. Total attempts: 4 Supply & Demand Demand refers to how much of a product or service is desired by buyers. The quantity demanded ${q}$ is the amount of a product people are willing to buy at a certain price ${p}$. Supply refers to how much of a product suppliers are willing to produce. The quantity supplied refers to the amount of a certain good producers are willing to supply ${q}$ when receiving a certain price ${p}$. Given the demand and supply functions below, find the following. Do not round your answers. Demand function: ${p}={1350}-{0.07}{{q}}^{{2}}$ Supply function: ${p}={0.09}{{q}}^{{2}}-{2}{q}$ Find the price when the quantity demanded is 50. Find the quantity supplied when the price is$1484.

#33 Points possible: 1. Total attempts: 4
Revenue function

A certain band charges $78 per ticket for concerts when 1260 people attend. The band members realize that for every$13 increase in the ticket price 21 fewer people will attend the concert. Find a revenue function ${R}$in terms of ${x}$ where ${x}$ represents the number of additional $13 increases in the ticket price. ${R}{\left({x}\right)}=$ What should the ticket price be for the band to maximize its revenue?$

How many people will attend the concert when the revenue is maximized?

What is the band's maximum revenue? \$

### pc5

Enter intro/instructions

#1 Points possible: 1. Total attempts: 4
Find the degree of the term ${5}$
Find the degree of the term ${1}{{x}}^{{4}}$
Find the degree of the term $-{6}{{x}}^{{6}}$
Find the degree of the term $-{4}{{x}}^{{7}}$
Find the degree of the polynomial ${5}+{1}{{x}}^{{4}}-{6}{{x}}^{{6}}-{4}{{x}}^{{7}}$

#2 Points possible: 1. Total attempts: 4
Find the degree of the polynomial ${y}={{x}}^{{7}}+{4}-{{x}}^{{5}}-{4}{{x}}^{{8}}$

#3 Points possible: 1. Total attempts: 4
Find the degree of the polynomial ${y}=-{{x}}^{{7}}+{4}{{x}}^{{6}}-{6}{{x}}^{{4}}-{2}$

#4 Points possible: 1. Total attempts: 4
Simply based on the degree of the polynomial ${y}=-{4}{{x}}^{{4}}-{1}{{x}}^{{8}}+{3}{{x}}^{{7}}+{2}$ find the maximum number of zeros (or roots, x-intercepts) and the maximum number of turning points (aka local extreme values, or peaks and valleys).

Maximum number of zeros:
Maximum number of turning points:

#5 Points possible: 1. Total attempts: 4
Find the degree of the polynomial ${y}={{\left({x}-{6}\right)}}^{{7}}{{\left({x}+{5}\right)}}^{{4}}{\left({x}+{1}\right)}$

#6 Points possible: 1. Total attempts: 4
Find the degree of the polynomial ${y}={{\left({x}+{1}\right)}}^{{5}}{{\left({x}+{6}\right)}}^{{3}}{{\left({x}+{4}\right)}}^{{2}}$

#7 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123-1-2-3

What is the least possible degree of the polynomial graphed above?

#8 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123-1-2-3

What is the least possible degree of the polynomial graphed above?

#9 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123-1-2-3

What is the least possible degree of the polynomial graphed above?

#10 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123456

What is the least possible degree of the polynomial graphed above?

#11 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123456

What is the least possible degree of the polynomial graphed above?

#12 Points possible: 1. Total attempts: 4
12345-1-2-3-4-5123456

What is the least possible degree of the polynomial graphed above?

#13 Points possible: 1. Total attempts: 4
The graph of ${f{{\left({x}\right)}}}={{x}}^{{3}}-{5}{x}-{2}$ is shown below.
Estimate the solution(s) to the equation ${f{{\left({x}\right)}}}=-{5}$.

1234-1-2-3-41234567891011-1-2-3-4-5-6-7-8-9-10-11

Enter solution(s) in the box below. If there is more than 1 solution, separate the values with a comma (example: -3, 2, 4.5).

#14 Points possible: 1. Total attempts: 4
The graph of ${y}={f{{\left({x}\right)}}}$ is shown below.
Estimate the solution(s) to the equation ${f{{\left({x}\right)}}}={1}$.

1234-1-2-3-41234567891011-1-2-3-4-5-6-7-8-9-10-11

Enter solution(s) in the box below. If there is more than 1 solution, separate the values with a comma (example: -3, 2, 4.5).

#15 Points possible: 1. Total attempts: 4
Suppose that the function ${f{{\left({x}\right)}}}$ is an even-degree polynomial. Also, its global (or end) goes to $\infty$. And, ${f}$ has the following turning points (peaks and valleys). Find the range of ${f}$ and express your answer in interval notation.

Turning points (points of peaks and valleys): ${\left(-{5},-{21}\right)}$ ; ${\left({1},{27}\right)}$${\left({23},-{13}\right)}$

Range:

 Subject Mathematics Due By (Pacific Time) 05/02/2013 12:00 am
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