Rise Placement Test Functions and Quadratic Equations 2

Question 1

Which of the following represents a function?

Accepted Answer

{(1,2),(2,3),(3,4)}

Answer

A relation is a function if each input (x-value) maps to exactly one output, which only {(1,2),(2,3),(3,4)} satisfies.

Question 2

What is the vertex of the parabola y = (x − 3)² + 5?

Accepted Answer

(3, 5)

Answer

In vertex form y = (x − h)² + k, the vertex is (h, k), so h = 3 and k = 5.

Question 3

If f(x) = 2x² − 3x + 1, what is f(−1)?

Accepted Answer

6

Answer

f(−1) = 2(1) − 3(−1) + 1 = 2 + 3 + 1 = 6.

Question 4

A quadratic equation has discriminant equal to 0. What does this mean?

Accepted Answer

One repeated real root

Answer

When the discriminant b² − 4ac = 0, there is exactly one repeated (double) real root.

Question 5

Which equation describes a parabola opening downward?

Accepted Answer

y = −3x² + 2x − 1

Answer

A parabola opens downward when the coefficient of x² is negative; −3 is negative.

Rise Placement Test Practice Test