Answer the questions about the following function. f(x) = 2x^2 - x -1.

Question

(a) Is the point (-2,9) on the graph of f?

(b) If x = 2 what is f(x)? What point is on the graph of f?

(c) If f(x) = -1, what is x? What points are on the graph of f?

(d) What is the domain of f?

(e) List the x-intercepts, if any, of the graph of f.

(f) List the y-intercept, if any, of the graph of f.

Answer 1

a) Verify 2(-2)²-(-2)-1 = 9

8+2-1 = 9

Yes

b) f(2) = 2(2)²-(2)-1 = 5

c) Set f(x) = -1 and solve for x

-1 = 2x²-x-1

x(2x-1) = 0

x =0, 1/2

(0,-1) and (1/2,-1) are on the graph

d) All real numbers

e) Factor f(x) = (2x+1)(x-1) --> x = 1, -1/2

f) Y-intercepts are found by setting x=0. --> f(0) = -1