Project #47778 - vertex and graphs algebra 1

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)

  1. 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.

    1. y = (x – 3)2 – 1

    2. y = (x – 2)2 + 4

  2. 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.

    1. y = (x – 5)2 – 3

    2. y = 2(x + 4)2 – 7

    3. y = –3(x + 1)2 + 2

    4. y = .5(x – 2)2

    5. y = (x – 1)2 + 1

    6. After you have decided for each graph, use the graphing calculator to check your decisions.

  3. 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.

  4. 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.

  1. y = (x – 3)2 – 4

  2. y = (x+2)2 – 25

  3. y = (x–3)2 – 9

  4. y = (x–5)2 + 1

  5. 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.

  1. Consider the graph of the equation y = (x – 7)(x + 3). How can you use the x-intercepts to help locate the vertex?

  2. 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).

  3. 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
Report DMCA

Chat Now!

out of 1971 reviews

Chat Now!

out of 766 reviews

Chat Now!

out of 1164 reviews

Chat Now!

out of 721 reviews

Chat Now!

out of 1600 reviews

Chat Now!

out of 770 reviews

Chat Now!

out of 766 reviews

Chat Now!

out of 680 reviews
All Rights Reserved. Copyright by - Copyright Policy