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

A. Is the point (-2,9) on the graph of f?
B. If x equals 2, what is fx? What point(S) are on the graph of f?
c. if f(x)= -1, what is x? what point(s) are on the graph of f?
d. what is the domain of f?
e. List the x-intercpts, if any, of the graph of f.
f. List the y-intercept if any, of the graph of f.

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1. Do you realize that
f(x) = 2x^2 - x - 1 and y = 2x^2 - x - 1 say the same thing ?

A) sub in the values x = -2 and y - 9 and see if they satisfy the equation
LS = 2(-2)^2 - (-2) - 1
= 8 + 2 + 1 = 9
RS = 9 = LS
Yes , the point (-2,9) does lie on the graph.

B) replace x with 2 and evaluate
C) f(x) = -1 is the same as saying y = -1
so 2x^2 - x - 1 = -1
2x^2 - x = 0
x(2x-1) = 0
x = 0 or x = 1/2
the two corresponding points are (0,-1) and (1/2, -1)
D) the domain of a function are the values of x that you may use in the equation. Can't we use any x we feel like ? , so the domain is the set of real numbers

E) at the x-intercept, y = 0
2x^2 - x - 1 = 0
(2x + 1)(x - 1) = 0
x = -1/2 or x = 1 -----> the two x-intercepts

F) for the y-intercept , let x = 0
y = 0 - 0 - 1 = -1

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