You have worked with quadratic functions in three forms:
Vertex or
Standard Form: Graphing Form: Factored Form
y=ax2 +bx+c y=a(x–h)2 +k y=a(x–p)(x–q)
Each of the following is in vertex form. Show how to rewrite each of these
functions in standard form and then, if possible, in factored form.
y = (x – 3)2 – 1
y = (x – 2)2 + 4
Without using the graphing calculator, sketch a rough graph of each equation below, and decide with your group (without using a graphing calculator) whether the graph of the equation has x-intercepts.
y = (x – 5)2 – 3
y = 2(x + 4)2 – 7
y = –3(x + 1)2 + 2
y = .5(x – 2)2
y = (x – 1)2 + 1
After you have decided for each graph, use the graphing calculator to check your decisions.
Write some rules about a, h, and k so that given this general quadratic
function in vertex form,
y=a(x–h)2 +k
you can determine how many x-intercepts it has without having to graph it.
If a quadratic function is given in vertex form how can you know the x- intercepts without having to draw the graph?
First discuss each function with your group and decide whether it has x- intercepts.
For each equation that you decide has x-intercepts, use algebra to rewrite the equation in factored form and explain how factored form tells you the x-intercepts.
• To check your work on a-e, use the graphing calculator to get the graph and locate the x-intercepts.
y = (x – 3)2 – 4
y = (x+2)2 – 25
y = (x–3)2 – 9
y = (x–5)2 + 1
y = (x–3)2 – 25
5. Use your graphing calculators, paper and pencil, and the help of your group. Look for connections between quadratic equations in vertex-form and quadratic equations in factored form.
Consider the graph of the equation y = (x – 7)(x + 3). How can you use the x-intercepts to help locate the vertex?
Experiment with other equations in factored form. Look for a way to locate the vertex of a parabola when you know the x-intercepts. Use your method on the equations y = (x– 8)(x–10) and y = 5(x+2)(x+4).
Describe a method for figuring out the vertex for the graph of equations that look like y = (x – p)(x – q).
Subject | Mathematics |
Due By (Pacific Time) | 11/16/2014 010:16 pm |
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