Rise Placement Test Functions and Quadratic Equations 5

Question 1

What is the minimum value of f(x) = x² − 6x + 10?

Accepted Answer

1

Answer

Completing the square: f(x) = (x−3)² + 1, so the minimum value is 1 at x = 3.

Question 2

Which equation has roots x = 4 and x = −1?

Accepted Answer

x² − 3x − 4 = 0

Answer

(x−4)(x+1) = x² − 3x − 4 = 0 has roots x = 4 and x = −1.

Question 3

A function f is defined as f(x) = x² for x ≥ 0. What is its inverse function?

Accepted Answer

f⁻¹(x) = √x

Answer

Swapping x and y in y = x² gives x = y², so y = √x for x ≥ 0.

Question 4

Completing the square on x² + 8x gives:

Accepted Answer

(x + 4)² − 16

Answer

x² + 8x = (x+4)² − 16 by adding and subtracting (8/2)² = 16.

Question 5

The height of a projectile is given by h = −5t² + 20t + 25. What is the initial height (t = 0)?

Accepted Answer

25 m

Answer

At t = 0: h = −5(0) + 20(0) + 25 = 25 meters.

Rise Placement Test Practice Test