EOC Expressions (Quadratic)

f(x) = (x - 5)² + 3

Which graph represents the quadratic function?

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Answer explanation

Graph (x, y) point for vertex is (5, 3)

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X-value for vertex (5) must have opposite sign (-5) in function

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Y-value for vertex (3) must have same sign (3) in function

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f(x) = (x - 5)² + 3

Function and graph match

Tags

CCSS.HSF-IF.C.7A

f(x) = (x + 5)² - 3

Which graph represents the quadratic function?

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• 
• 
• 

Answer explanation

Graph (x, y) point for vertex is (-5, -3)

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X-value for vertex (-5) must have opposite sign (5) in function

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Y-value for vertex (-3) must have same sign (-3) in function

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f(x) = (x + 5)² - 3

Function and graph match

Tags

CCSS.HSF-IF.C.7A

Which of the following quadratic functions has the vertex (2, 4)?

• f(x) = 4(x − 2)² + 4

• f(x) = 3(x + 2)² + 4

• f(x) = 2(x − 4)² + 2

• f(x) = 2(x + 4)² + 2

Answer explanation

Graph (x, y) point for vertex is (2, 4)

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X-value for vertex (2) must have opposite sign (-2) in function

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Y-value for vertex (4) must have same sign (4) in function

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f(x) = a(x - 2)² + 4

Function and graph match

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f(x) = 4(x − 2)² + 4

This is correct option

f(x) = 3(x − 5)² + 7

What is the vertex of the following quadratic function?

• (7, -5)

• (5, 7)

• (3, 5)

• (-5, 7)

Answer explanation

f(x) = 3(x − 5)² + 7

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You can graph the function to see the vertex is (5, 7), or you could interpret the function without graphing

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X-value for vertex (5) must have opposite sign (-5) in function

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Y-value for vertex (7) must have same sign (7) in function

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(5, 7) is the vertex point

f(x) = x² – 12x + 9

What is the vertex of the following quadratic function?

• (6, -27)

• (-12, 9)

• (12, -9)

• (-6, -27)

Answer explanation

f(x) = x² – 12x + 9

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You can graph the function to see the vertex is (6, -27)

f(x) = x² – 12x + 9

What is the vertex form of the following quadratic function?

• f(x) = (x - 6)² - 27

• f(x) = (x + 6)² - 27

• f(x) = (x - 6)² + 27

• f(x) = (x + 6)² + 27

Answer explanation

f(x) = x² – 12x + 9

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You can graph the function to see the vertex is (6, -27)

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X-value for vertex (6) must have opposite sign (-6) in new function

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Y-value for vertex (-27) must have same sign (-27) in new function

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f(x) = (x - 6)² - 27

f(x) = -3(x + 4)² + 2

Find the maximum or minimum of the graph of the quadratic function.

• Max: 2

• Min: 2

• Max: 4

• Min: 4

• Max: -4

Answer explanation

f(x) = -3(x + 4)² + 2

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Graph (x, y) point for vertex is (-4, 2)

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The y-value for the vertex is the maximum value on graph (the highest point)

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Max: y = 2

f(x) = x² + 6x + 8

What are the zeros for the function above?

(select two answers)

• 1

• 6

• 8

• -4

• 2

Answer explanation

f(x) = x² + 6x + 8

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Zeros refers x-intercepts

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Graph shows two x-intercepts

(-4, 0) and (-2, 0)

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The x-value for each x-intercept point (x, y) is the zero

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x = -4 and x = -2 are the zeros

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

f(x) = x² + 6x + 8

What is the factored form of the following quadratic function?

Answer explanation

f(x) = x² + 6x + 8

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x = -4 and x = -2 are the zeros found on previous question

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Use opposite sign of each zero in formula for r-values

f(x) = (x - r₁)(x - r₂)

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f(x) = (x + 4)(x + 2)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

f(x) = x² - 2x - 15

What is the factored form of the following quadratic function?

Answer explanation

f(x) = x² - 2x - 15

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x = -3 and x = 5 are the zeros found on previous question

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Use opposite sign of each zero in formula for r-values

f(x) = (x - r₁)(x - r₂)

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f(x) = (x + 3)(x - 5)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A