7-1 REVIEW Miss battaglia – algebra 1 CP Objective: Graph quadratic functions of the form y=ax^2

7-1 re

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Miss b

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CP

Object

ive: G

raph q

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tic fu

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ns of t

he fo

rm y

=ax^2

Warm up

What are some real life examples of parabolas? (Ex: smile, mountain)

Quadratic functions

The graphs from the warm up are all parabolas. If you draw a parabola on a piece of paper, you can fold the paper down the middle of the parabola and the two sides will match exactly. The line down the middle of the parabola is the axis of symmetry.

Draw the axis of symmetry

Quadratic function

example

Name the values of a, b, and c for each quadratic equation.

a. y = 2x + 4x2 + 10 b. y = 2 + x2

Write each quadratic function in standard form.

a.y = 2x2 + 6x b. y = -3 + 2x2 + x

Make a table of values & graph the quadratic functions

x y = 3x2 y = - 4x2

-3

-2

-1

0

1

2

3

y = 3x2 and y = - 4x2

The highest or lowest point on a parabola is called the vertex of the parabola.

When a parabola opens upward, the y-coordinate

of the vertex is the minimum value of the

function.

When a parabola opens downward, the y-

coordinate of the vertex is the maximum value of

the function.

example

Answer these questions for y = -2x2 and y = 8x2

a.What is the value of a?

b.In which direction does each graph open?

a.Is the y-coordinate of the vertex a minimum or a maximum value of the function?

Use a graphing calculator

example

Order each group of quadratic functions from widest to narrowest graph.

y = x2, y = x2, y = x2

classwork

homework