Question

Given the function f(x) =2xsquared - x-1
(a) Is the point (-1, 2) 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) 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 .

Answer 1

(a) Yes, the point (-1, 2) on the graph of f because $f(−1)=2∗(−1)^2−(−1)−1=2+1-1=2.$

(b) If $x=−2$ then $f(−2)=2∗(−2)^2−(−2)−1=2*4+2-1=9.$

Point (-2, 9) is on the graph of f.

(c) If $f(x)=−1$ then $2x^2−x−1=−1$, $2x^2-x=0$, $x(2x−1)=0,$ $x=0$ or $x=0.5$.

Points (0, -1) and (0.5, -1) are on the graph of f.

(d) f is a quadratic function, its domain is all real numbers.

(e) In order to find x-intercepts of the graph of f we take y=0 and solve the quadratic equation: $2x^2−x−1=0$ .

$a=2, b=−1, c=−1$ .

$x=\frac{1\pm \sqrt{(-1)^2-4*2*(-1)}}{2*2}.$

$x=\frac{1\pm 3}{4}$ .

$x=−0.5$ or $x=1.$

So we have two x-intercepts of the graph of f: (-0.5, 0) and (1, 0).