AlgebraAlgebra

9.3 9.3

Graphing Quadratic FunctionsGraphing Quadratic Functions

CLASSIFYING EQUATIONSCLASSIFYING EQUATIONS

LINEAR QUADRATIC

y = 2x + 4y = 2x²+ 7x + 3

y = 5x²y = 5x

y = x² - 4y = x - 4

What is the pattern ?

Standard Form of a Quadratic Equation

y = ax²+ bx + c (a ≠ 0)

An equation is called QUADRATIC if it has a squared variable

There may or may not be the “middle term” or the constant.

There MUST be a squared variable.

Every quadratic function has a U-shaped graph

called a parabola.

The vertex of a parabola is the lowest point of a parabola that opens up and the highest point of a parabola that opens down.

vertex

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vertex

●

vertex

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vertex

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The axis of symmetry of a parabola is the line passing through the vertex that divides the parabola into two symmetric parts.

axis of symmetry axis of symmetry

Identifying a, b and c

In y = 2x²+ 3x – 5

y = ax²+ bx + c (a ≠ 0)

a = 2 b = 3 c = -5

In y = -x²- 5x + 2 a = -1 b = -5 c = 2

In y = x²- 3x a = 1 b = -3 c = 0

In y = -x²+ 4 a = -1 b = 0 c = 4

In y = -3x² a = -3 b = 0 c = 0

The effect of a on the parabola

If a is positivethe parabola opens up

If a is negativethe parabola opens down

y = x²+ 2x + 1 y = -x²+ 2x + 1a = 1 a = -1

Finding the vertex

In y = x²+ 4x + 8

In the equation y = ax²+ bx + c the x coordinate of the vertex

a = 1 b = 4 c = 8

●

can be found using the formula:

bx =-

2a

VERTEX: x = 4

22 2(1)

b

a

Then substitute the x value into the original equation to find the y coordinate

y = (-2)² + 4(-2) + 8

y = 4 -8 + 8 = 4VERTEX: (-2, 4)

Graphing a Quadratic Function

b-

2a

STEPS

1. Find the x coordinate of the vertex:

x =Draw the line of symmetry at the x-value.

Then substitute the x value to find y.The vertex will be an ordered pair (x,y).

2. Make an x/y table. Choose x values to the left and right of the vertex. Plot as you go.

3. Connect the points as a smooth curve.

x y

Graph: y = x²- 2x - 3

-1 0

0 -3

2 -3

3 0

x

y

Vertex: x =b

-2a

- 2-

2(1)= = 1

y = (1)² - 2(1) – 3 = -4

1 -4

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x y

Graph: y = -x²+ 2x - 3

-1 -6

0 -3

2 -3

3 -6

x

y

Vertex: x =b

-2a

2-

2(- 1)= = 1

y = -(1)² + 2(1) – 3 = -2

1 -2

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A Few together from the A Few together from the HomeworkHomework

pg. 521 # 5 and #15

HomeworkHomework

pg. 521 # 1-15