warm up simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 4

WARM UP

Simplify1. 62

2. (-14)2

3. -92

4. -4x2, for x = 3

4

WARM UP

Simplify1. 62

2. (-14)2

3. -92

4. -4x2, for x = 3

3

WARM UP

Simplify1. 62

2. (-14)2

3. -92

4. -4x2, for x = 3

2

WARM UP

Simplify1. 62

2. (-14)2

3. -92

4. -4x2, for x = 3

1

Simplify1. 62

2. (-14)2

3. -92

4. -4x2, for x = 3

WARM UP 0

A quadratic function is a function that can be written in the standard form

y = ax2 + bx + c

Every quadratic function has a U-shaped graph called a parabola. The parabola opens up if the value of a is positive. The parabola opens down if the value of a is negative.

9.4 Graphing Quadratic Functions

GOAL•Sketch the graph of a quadratic functionKEY WORDS•Quadratic function•Parabola•Vertex•Axis of symmetry


EXAMPLE 1 Describe the Graph of a Parabola

a) The graph of y = x2 opens up.The lowest point is (0, 0).

b) The graph of y = –x2 + 4 opens down.The highest point is (0, 4).


Checkpoint Describe the Graph of a ParabolaDecide whether the parabola opens up or down.1. y = -x2

2. y = 2x2 - 4 3. y = -3x2 + 5x - 1


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

The vertical line passing through the vertex that divides the parabola into two symmetric parts is called the axis of symmetry. The two symmetric parts are mirror images of each other.


GRAPHING A QUADRATIC FUNCTIONThe graph of y = ax2 + bx + c is a parabola.STEP 1 Find the x-coordinate of the vertex, which is x = - STEP 2 Make a table of values, using x-values to the left and right of the vertex.STEP 3 Plot the points and connect them with a smooth curve to form a parabola.


a

b

2

EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of y = x2 - 2x – 3SOLUTION In this quadratic function, a =1, b = -2, and c = -3. STEP 1 Find the x-coordinate of the vertex

-

=

= 1


a

b

2

)1(2

2

EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of y = x2 - 2x – 3SOLUTION In this quadratic function, a =1, b = -2, and c = -3. STEP 2 Make a table of values, using x-values to the left and right of x=1


x -2 -1 0 1 2 3 4

y

EXAMPLE 2 Graph Quadratic Function with Positive a-ValueSketch the graph of y = x2 - 2x – 3SOLUTION In this quadratic function, a =1, b = -2, and c = -3. STEP 3 Plot the points.

The vertex is (1, -4).

Connect the points to form a parabolathat opens up since a is positive.

The axis of symmetry passes through thevertex . The x-coordinate of the vertex is1, and the axis of symmetry is the verticalline x = 1.


Checkpoint Graph a Quadratic Function with a Positive a-Value

Sketch the graph of the function. Label the coordinates of the vertex.1. y = x2 + 22. y = 2x2 – 4x - 1 3. y = x2 + 2x


EXAMPLE 3 Graph Quadratic Function with Negative a-ValueSketch the graph of y = -x2 - 3x + 1SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. STEP 1 Find the x-coordinate of the vertex

-

=

= - or -1.5


a

b

2

)1(2

3

2

3

EXAMPLE 2 Graph Quadratic Function with Negative a-ValueSketch the graph of y = -x2 - 3x + 1SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. STEP 2 Make a table of values, using x-values to the left and right of x=1


x -4 -3 -2 -1.5 -1 0 1

y

EXAMPLE 2 Graph Quadratic Function with Negative a-ValueSketch the graph of y = -x2 - 3x + 1SOLUTION In this quadratic function, a =-1, b = -3, and c = 1. STEP 3 Plot the points.

The vertex is (-1.5, 3.25).

Connect the points to form a parabolathat opens down since a is negative.

To find the y-intercept of y = -x2 - 3x + 1,let x = 0. The y-intercept is 1.


YOU’RE CERTIFIED!Page 523#s 15 -32


warm up simplify 1.6 2 2.(-14) 2 3.-9 2 4.-4x 2, for x = 3 4

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