6.1 Graphing Quadratic Functions

Parabola

Axis of symmetry

Vertex

A Quadratic function

Parts of the Quadratic function.

CONSTANT TERM

0,2 awherecbxaxxf

termquadratic

termlinear

The graph of a Quadratic function is called a parabola.

A Quadratic function

Parabola are Symmetrical

Axis of Symmetry, splits it down the middle

Parabola are Symmetrical

Points reflect across the axis of symmetry

5,4 5,0

2,3 2,1

Parabola are Symmetrical

The equation for the axis symmetry is

5,4 5,0

2,3 2,1

a

bx

2

The y – Intercept of a parabola

If x = 0, then c is the y intercept

0,)0()0(0 2 xwherecbaf

4)0(

4)0(6)0(3)0(

463)(

2

2

f

f

xxxf

The Vertex of the Parabola

The Vertex is a point at the highest or lowest point of the graph of a parabola. The Vertex is on the axis of symmetry, so its x coordinate is found by

a

bx

2

242)(

)(

2

2

xxxf

cbxaxxf

1)2(2

)4(

x

Now that you have x of the Vertex how do you find the y

x = 1 242)( 2 xxxf

0)1(

242)1(

2)1(4)1(2)1( 2

f

f

f

0,1

How can you tell if the Vertex is the highest or lowest point.

It all depends on “a”.

If a > 0, the parabola If a<0, the parabola is opens upward. opens downward

The Maximum or Minimum value is the y value of the vertex

If the vertex is ( -3, 1), of f(x)= x2 + 6x + 10, then the minimum value is 1. Since the

parabola is opening upward it is the minimum.

1,3

How to graph the parabolaf(x) = 2- 4x + x2

Rewrite the function. f(x) = x2 -4x + 2Find the y intercept: f(0) = 02 -4(0) + 2 = 2

(0, 2)

Find the vertex: a = 1, b= -4

2,22)2(

224)2()2(

2)1(2

)4(

2

f

f

x

How to graph the parabolaf(x) = 2- 4x + x2

Start a table using number higher and lower then 2, from the vertex. Plot points

How to graph the parabolaf(x) = 2- 4x + x2

Connects the points.

Graph the function. Show the y intercept, axis of symmetry and vertex

f(x) = -x2 + 2x + 3

Graph the function. Show the y intercept, axis of symmetry and vertex

f(x) = -x2 + 2x + 3

Does the graph open up or down?

What are a , b and c?

Graph the function. Show the y intercept, axis of symmetry and vertex

f(x) = -x2 + 2x + 3

Does the graph open up or down? Down

What are a , b and c?

a = -1

b = 2

c = 3, so the y intercept is (0,3)

Graph the function. Show the y intercept, axis of symmetry and vertex

f(x) = -x2 + 2x + 3

axis of symmetry is x = 1

What are a , b and c?

a = -1 The vertex is

b = 2

c = 3

4,14)1(

312)1()1(

1)1(2

)2(

2

f

f

x

Graph the function. Show the y intercept, axis of symmetry and vertex

f(x) = -x2 + 2x + 3

Plot the points

Graph the function. Show the y intercept, axis of symmetry and vertex

f(x) = -x2 + 2x + 3

Connect the points

Homework

Page 291

# 15, 19, 23, 25,

33 – 43 odd

Homework

Page 291- 292

# 16, 22, 26,

32 - 42 even, 46, 47