Rise Placement Test Functions and Quadratic Equations 3

Question 1

Using the quadratic formula, what are the solutions to x² + 4x + 3 = 0?

Accepted Answer

x = −1 and x = −3

Answer

Factoring gives (x+1)(x+3) = 0, so x = −1 or x = −3.

Question 2

What is the domain of f(x) = √(x − 4)?

Accepted Answer

x ≥ 4

Answer

The expression under the square root must be non-negative, so x − 4 ≥ 0, giving x ≥ 4.

Question 3

If g(x) = x² − 4x + 4, what is g(x) in factored form?

Accepted Answer

(x − 2)²

Answer

x² − 4x + 4 is a perfect square trinomial equal to (x − 2)².

Question 4

A ball is thrown upward with height h(t) = −16t² + 64t. At what time does it reach its maximum height?

Accepted Answer

t = 2 sec

Answer

The vertex time is t = −b/(2a) = −64/(2·(−16)) = 2 seconds.

Question 5

Which transformation moves the graph of f(x) = x² three units to the right?

Accepted Answer

f(x) = (x−3)²

Answer

Replacing x with (x − 3) shifts the graph 3 units to the right.

Rise Placement Test Practice Test