given the function f(x)=2x^2-x-1

Question

f(x)=2x^2-x-1

A. Is th 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 point(s) ar on the graph of f?

D. what is the domain of f

E.list the x-intercept(s), if any of the graph of f

F. list the y-intercept, if any, of the graph of f

Answer 1

A

f(-2) = 2(-2)^2 -(-2) -1

f(-2) = 2(4) +4 -1

f(-2) = 8 +4 -1

f(-2) = 11

No, the point (-2,9) is not on the graph of f.

B

f(2) = 2(2^2) -2 -1

f(2) = 2(4) -2 -1

f(2) = 8 -2 -1

f(2) = 5

(2,5) is on the graph of f.

C

f(x) = -1

2x^2 -x -1 = -1

2x^2 -x = 0

x * (2x -1) = 0

x = 0 or 1/2

The points (0,-1) and (1/2,-1) are on the graph of f.

D

Domain is possible x values.  There's nothing funny- no square roots or fraction bars- so there's nothing that says x can't be something.

Domain is all real numbers.

E

x-intercepts >> f(x) = 0

2x^2 -x -1 = 0

(2x    ) (x    )

(2x   1) (x   1)

(2x + 1) (x - 1) = 0

x = -1/2 and x = 1

x-intercepts at x = -1/2 and x = 1

F

y-intercepts >> x=0

f(0) = 2(0^2) -0 -1

f(0) = -1

y-intercept at y -1

You can see a graph of it by typing this into Google:  plot(2x^2-x-1)