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6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex

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6.1 Graphing Quadratic Functions. Parabola Axis of symmetry Vertex. A Quadratic function. Parts of the Quadratic function. CONSTANT TERM. A Quadratic function. The graph of a Quadratic function is called a parabola. Parabola are Symmetrical. Axis of Symmetry, splits it down the middle. - PowerPoint PPT Presentation

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Page 1: 6.1 Graphing Quadratic Functions

6.1 Graphing Quadratic Functions

Parabola

Axis of symmetry

Vertex

Page 2: 6.1 Graphing Quadratic Functions

A Quadratic function

Parts of the Quadratic function.

CONSTANT TERM

0,2 awherecbxaxxf

termquadratic

termlinear

Page 3: 6.1 Graphing Quadratic Functions

The graph of a Quadratic function is called a parabola.

A Quadratic function

Page 4: 6.1 Graphing Quadratic Functions

Parabola are Symmetrical

Axis of Symmetry, splits it down the middle

Page 5: 6.1 Graphing Quadratic Functions

Parabola are Symmetrical

Points reflect across the axis of symmetry

5,4 5,0

2,3 2,1

Page 6: 6.1 Graphing Quadratic Functions

Parabola are Symmetrical

The equation for the axis symmetry is

5,4 5,0

2,3 2,1

a

bx

2

Page 7: 6.1 Graphing Quadratic Functions

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

Page 8: 6.1 Graphing Quadratic Functions

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

Page 9: 6.1 Graphing Quadratic Functions

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

Page 10: 6.1 Graphing Quadratic Functions

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

Page 11: 6.1 Graphing Quadratic Functions

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

Page 12: 6.1 Graphing Quadratic Functions

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

Page 13: 6.1 Graphing Quadratic Functions

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

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

Page 14: 6.1 Graphing Quadratic Functions

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

Connects the points.

Page 15: 6.1 Graphing Quadratic Functions

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

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

Page 16: 6.1 Graphing Quadratic Functions

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?

Page 17: 6.1 Graphing Quadratic Functions

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)

Page 18: 6.1 Graphing Quadratic Functions

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

Page 19: 6.1 Graphing Quadratic Functions

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

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

Plot the points

Page 20: 6.1 Graphing Quadratic Functions

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

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

Connect the points

Page 21: 6.1 Graphing Quadratic Functions

Homework

Page 291

# 15, 19, 23, 25,

33 – 43 odd

Page 22: 6.1 Graphing Quadratic Functions

Homework

Page 291- 292

# 16, 22, 26,

32 - 42 even, 46, 47