Rise Placement Test Functions and Quadratic Equations 4

Question 1

What is the axis of symmetry for y = 2x² − 12x + 7?

Accepted Answer

x = 3

Answer

The axis of symmetry is x = −b/(2a) = −(−12)/(2·2) = 3.

Question 2

The function f(x) = x² − 2x − 15 crosses the x-axis at which points?

Accepted Answer

x = 5 and x = −3

Answer

Factoring gives (x−5)(x+3) = 0, so x = 5 or x = −3.

Question 3

If f(x) = 3x + 2 and g(x) = x², what is f(g(2))?

Accepted Answer

14

Answer

g(2) = 4, then f(4) = 3(4) + 2 = 14.

Question 4

How many real solutions does 3x² + 2x + 5 = 0 have?

Accepted Answer

No real solutions

Answer

The discriminant is 4 − 60 = −56 < 0, so there are no real solutions.

Question 5

Which point is on the graph of f(x) = x² − 3x + 2?

Accepted Answer

(1, 0)

Answer

f(1) = 1 − 3 + 2 = 0, so (1, 0) is on the graph.

Rise Placement Test Practice Test