Notes Over 9.3Graphs of Quadratic Functions

Standard form of a Quadratic is:

y ax bx c 2

The graph of a quadratic is a Parabola.

The Vertex of a parabola is the lowest point that opens up, or the highest point that opens down.

The Axis of Symmetry of a parabola is the vertical line passing through the vertex.

Notes Over 9.3Sketching a Quadratic FunctionSketching a Quadratic Function

17122 2 xxy

y

a

b,

2

2 a

b

Vertex:

12 2

12

43 3,

17 12 2 2 y 3 3 2y 9 36 17

y 18 19 1

1

Notes Over 9.3Sketching a Quadratic FunctionSketching a Quadratic Function

17122 2 xxy Vertex: 3, 1Since a is –2, it will go down twice as fast as normal.

2

The normal graph is from y = x2

when x goes out 1, y goes up 1; when x goes out 2, y goes up 4; when x goes out 3, y goes up 9

So go down twice as fast as normal

Notes Over 9.3Sketching a Quadratic Function with a Positive a-valueSketching a Quadratic Function with a Positive a-value

22 1 xy .

2 a

b

Vertex:

0

2

0

40

0,

2 2y 0 0y

0

Notes Over 9.3Sketching a Quadratic Function with a Positive a-valueSketching a Quadratic Function with a Positive a-value

xxy 3 2 2 .

2 a

b

Vertex:

3

1

3

2

2

3,

3 2 y2

3

4

9y

4

9

2

3

2

9

4

18

4

9

Normal Graph

Notes Over 9.3Sketching a Quadratic Function with a Positive a-valueSketching a Quadratic Function with a Positive a-value

12 3 2 xxy.

2 a

b

Vertex:

2

1

2

2

1,

1 2 2 y 1

1y

0

1

2 1Normal Graph

0

Notes Over 9.3Sketching a Quadratic Function with a Negative a-valueSketching a Quadratic Function with a Negative a-value

24 4 xy .

2 a

b

Vertex:

0

40

8

0

0,

2 4y 0 0y

0

Notes Over 9.3Sketching a Quadratic Function with a Negative a-valueSketching a Quadratic Function with a Negative a-value

xxy 2 5.

2 a

b

Vertex:

1

11

2

2

1,

2 y2

1

4

1y

4

1

2

1

2

1

4

2

4

1

Normal Graph

Notes Over 9.3Sketching a Quadratic Function with a Negative a-valueSketching a Quadratic Function with a Negative a-value

32 6 2 xxy.

2 a

b

Vertex:

2 1

2

2

1,

3 2 2 y 1

1y

4

1

2 3Normal Graph

4

Notes Over 9.3Using a Quadratic ModelUsing a Quadratic Model

7. A ball was thrown and followed a path described by: , What was the maximum height (in feet) of the thrown ball?

xxy 2010.

xb

a

2

1

0 01.b g1

50

y 0 012

. b gb g50 50

25 feet

The maximum height occurred at the vertex.

0 02.

50 25

Notes Over 9.3