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GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

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Page 1: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

GRAPHING QUADRATIC FUNCTIONS

VERTEX FORM

Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum

value. (A-SSE.3b)

Page 2: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

VOCABULARY: Parabola-

Vertex-

Axis of symmetry-

The U-shaped graph of a quadratic function

The highest (maximum) or lowest (minimum) point on a parabola

The vertical line that passes through the vertex and divides the parabola into 2 equal parts

Page 3: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

VERTEX FORM OF A QUADRATIC FUNCTION

Given the function y = a(x – h)2 + k If a > 0, the parabola opens up If a < 0, the parabola opens down The axis of symmetry is x = h The vertex is (h, k)

Page 4: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

VERTEX FORM OF A QUADRATIC FUNCTION

Page 5: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

EXAMPLE Determine the a to decide if the parabola opens up

or down or it’s a minimum or maximum, the coordinates of the vertex and the line of symmetry.

23 2y x

3x 3,2

:a 1

:Opens Up

Minimum

:Vertex

:Line of Symmetry

Now let’s Graph!

Page 6: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

2. Make a table of values:

EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.

X Y

vtx

-2

-5-4-3

-1

y = (-5 +3)2 + 26

3

2

3

6

y = (-4 +3)2 + 2

y = (-2 +3)2 + 2y = (-1 +3)2 + 2

23 2y x

Now let’s Graph!

3. Plot points:

Page 7: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

EXAMPLE Determine the a to decide if the parabola opens up

or down or it’s a minimum or maximum, the coordinates of the vertex and the line of symmetry.

2x 2, 6

:a 1

:Opens Up

Minimum

:Vertex

:Line of Symmetry

Now let’s Graph!

22 6y x

Page 8: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

2. Make a table of values:

EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.

X Y

vtx

-1

-4-3-2

0

y = (-4 +2)2 - 6-2

-5

-6

-5

-2

y = (-3 +2)2 - 6

y = (-1 +2)2 - 6y = (0 +2)2 - 6

Now let’s Graph!

3. Plot points:

22 6y x

Page 9: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

EXAMPLE Determine the a to decide if the parabola opens up

or down or it’s a minimum or maximum, the coordinates of the vertex and the line of symmetry.

3x 3,0

:a 4:Opens Down

Maximum

:Vertex

:Line of Symmetry

Now let’s Graph!

24 3y x

Page 10: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

2. Make a table of values:

EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.

X Y

vtx

4

1

23

5

y = -4(1 -3)2

-16

-4

0

-4

-16

y = -4(2 -3)2

y = -4(4 -3)2

y = -4(5 -3)2

Now let’s Graph!

3. Plot points:

24 3y x

Page 11: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

CHANGE A QUADRATIC FUNCTION FROM STANDARD FORM TO VERTEX FORM

Move the constant

Add (b/2)2 to each side

Factor the perfect square trinomial

Write in the form y = a(x – h)2 + k

2 4 6y x x 26 4y x x 26 4 4 4y x x

22 2y x

22 2y x

Now let’s Graph!

Page 12: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

2. Make a table of values:

EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.

X Y

vtx

-1

-4-3-2

0

y = (-4 +2)2 + 26

3

2

3

6

y = (-3 +2)2 + 2

y = (-1 +2)2 + 2y = (0 +2)2 + 2

Now let’s Graph!

3. Plot points:

22 2y x

Page 13: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

WRITE THE QUADRATIC IN VERTEX FORM

Move the constant

Add (b/2)2 to each side

Factor the perfect square trinomial

Write in the form y = a(x – h)2 + k

2 4 1y x x 21 4y x x 21 4 4 4y x x

25 2y x

22 5y x

Now let’s Graph!

Page 14: GRAPHING QUADRATIC FUNCTIONS VERTEX FORM Goal: I can complete the square in a quadratic expression to reveal the maximum or minimum value. (A-SSE.3b)

2. Make a table of values:

EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.

X Y

vtx

3

0

1

2

4

y = (0 -2)2 - 5-1

-4

-5

-4

-1

y = (1 -2)2 - 5

y = (3 -2)2 - 5

y = (4 -2)2 - 5

Now let’s Graph!

3. Plot points:

22 5y x