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Warmup Tuesday, February 27, 2024

Use completing the square to convert from standard form to to vertex form.

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Change Standard Form to Vertex Form by Completing the Square

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Convert to vertex form practice sheet
Delta Math: Convert to vertex form (finish for homework)

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Domain and Range

Domain is always: _ _
If “a” is positive, then the graph opens _ _ and the range is y > k
If “a” is negative, then the graph opens _ _ and the range is y < k

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Domain and Range

Domain is always: _ all real numbers _
If “a” is positive, then the graph opens _ up _ and the range is y > k
If “a” is negative, then the graph opens _ down _ and the range is y < k

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Identify the Vertex, Domain and Range

24) y = (x - 3)² - 3

a = ______ h = ______ k = ______

Opens ________ Vertex (____ ,____)

Axis of symmetry: ___________

Domain: ____________________________

Range: __________________

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Identify the Vertex, Domain and Range

24) y = (x - 3)² - 3

a = ___1___ h = ___3___ k = __-3____

Opens __up____ Vertex (_3__ ,_-3__)

Axis of symmetry: ___x = 3____

Domain: ____all real numbers________

Range: _____y ≥ -3_____

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Identify the Vertex, Domain and Range

25) y = -½(x - 4)² + 3

a = ______ h = ______ k = ______

Opens ________ Vertex (____ ,____)

Axis of symmetry: ___________

Domain: ____________________________

Range: __________________

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Identify the Vertex, Domain and Range

25) y = -½(x - 4)² + 3

a = __-1/2___ h = ___4___ k = __3____

Opens __down____ Vertex (_4__ ,_3__)

Axis of symmetry: ___x = 4____

Domain: ____all real numbers________

Range: _____y ≤ -3_____

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Identify the Vertex, Domain and Range

26) y = (x - 1)² + 2

a = ______ h = ______ k = ______

Opens ________ Vertex (____ ,____)

Axis of symmetry: ___________

Domain: ____________________________

Range: __________________

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Identify the Vertex, Domain and Range

26) y = (x - 1)² + 2

a = ___1___ h = ___1___ k = __2____

Opens __up____ Vertex (_1__ ,_2__)

Axis of symmetry: ___x = 1____

Domain: ____all real numbers________

Range: _____y ≥ 2_____

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a. y = -(x - 3)² - 3 Opens: __________ Vertex: (____ ,____) Axis of symmetry: __________ Domain: ______________________ Range: __________	b. y = -4(x - 8)² Opens: __________ Vertex: (____ ,____) Axis of symmetry: __________ Domain: ______________________ Range: __________	c. y = ⅔(x + 2)² + 10 Opens: __________ Vertex: (____ ,____) Axis of symmetry: __________ Domain: ______________________ Range: __________

27. Try these on your own.

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a. y = -(x - 3)² - 3 Opens: ___down___ Vertex: (__3_ ,_-3_) Axis of symmetry: __x = 3___ Domain: ___all real numbers____ Range: ___y ≤ -3___	b. y = -4(x - 8)² Opens: __down__ Vertex: (__8_ ,_0_) Axis of symmetry: __x = 8__ Domain: ____all real numbers____ Range: __y ≤ 0___	c. y = ⅔(x + 2)² + 10 Opens: _up___ Vertex: (__-2_ ,_10_) Axis of symmetry: __x = -2__ Domain: ____all real numbers____ Range: _y ≥ 10____

27. Try these on your own.

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Domain:

Range:

Domain:

Range:

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Domain: All Real Numbers

Range: y ≤ 7

Domain: All Real Numbers

Range: y ≥ -1

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Find the domain and range of the parabolas around the room

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A

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A

Domain: All Real Numbers

Range:

y ≤ 4

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B

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B

Domain: All Real Numbers

Range:

y ≤ 1

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C

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C

Domain: All Real Numbers

Range:

y ≥ -4

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D

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D

Domain: All Real Numbers

Range:

y ≤ 9

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E

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E

Domain: All Real Numbers

Range:

y ≥ -9

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F

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F

Domain: All Real Numbers

Range:

y ≥ -1

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Finish Delta Math: Convert to vertex form

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28. y = x² + 2x + 1

Vertex:

(_____, _____)

Axis of Symmetry: ____________

x	y

Graph the quadratic equation using vertex and table of values.

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28. y = x² + 2x + 1

Vertex:

(_-1__, __0__)

Axis of Symmetry: ____x = -1___