Topic 2 - Quadratic Functions and Equations

The function h(x) = − 1/2(x − 4)² + 3 represents the height of a bird y over time x , as it flies past the school. What point on the graph represents the greatest height of the bird above the ground?

• (4, 3)

• (3, 4)

• (1/2 , 4)

• (3, 1/2)

Tags

CCSS.HSF-IF.C.7A

What is the equation written in vertex form of a parabola with a vertex of (9, −1) that passes through (7, 7) ?

• y = 2 (x − 9)² − 1

• y = 2 (x + 1)² − 9

• y = 2 (x − 7)² + 7

• y = 7 (x − 9)² − 1

Function g is a transformation of the parent function f(x) = x² . The graph of g is a translation right 3 units and down 5 units of the graph of f . What is the equation of function g written in the form y = ax² + bx + c ?

• y = x² + 6x + 4

• y = x² − 6x + 4

• y = x² + 10x + 22

• y = x² − 6x + 14

What is the minimum point of the graph of the function f(x) = x² − 4x ?

• 𝖠 (2, 4)

• (0, 0)

• (4, 0)

• (2, −4)

A pebble is tossed into the air from the top of a cliff. The height, in feet, of the pebble over time is modeled by the equation y = −16x² + 32x + 80 . What is the maximum height, in feet, reached by the pebble?

Mathematical Equivalence

ON

What is the equation of a parabola that passes through the points (−5, −10) , (−1, 6) , and (2, −3) ?

• y = −x² − 2x + 5

• y = −x² + 6x − 7

• y = −x² − 3x + 2

Factor the expression 3x² − 11x − 4 .

(​ (a)   x + ​ (b)   )(x - ​ (c)   )​

• 3
• 1
• 4
• 2
• -1
• -4

A projectile is launched into the air. The function h(t) = −16t² + 32t + 128 gives the height, h , in feet, of the projectile t seconds after it is launched. After how many seconds will the projectile land back on the ground?

Mathematical Equivalence

ON

Identify the intervals on which the function f(x) = x² + 12x + 27 is positive.

(​ (a)   , ​ (b)   ) and ( ​ (c)   , ​ (d)   )​

• - inf
• - 9
• - 3
• + inf
• 3
• 9

Use square roots to solve the equation x² = −64 over the complex numbers.

Select all solutions that apply.

• 8i

• • −8

• −8i²

• 8i²

• −8i

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7