Answer
(a) The graph of the equation $y=4x^2-1$ is as shown.
(b) The $x$-intercepts are $\left(-\frac{1}{2},0\right)$ and $\left(\frac{1}{2},0\right)$.
(c) The solution is $x=-\frac{1}{2},\frac{1}{2}$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
Work Step by Step
(a) The graph of the equation $y=4x^2-1$ is as shown.
(b) The $x$-intercepts are $\left(-\frac{1}{2},0\right)$ and $\left(\frac{1}{2},0\right)$.
(c) Setting $y=0$:
$$0=4x^2-1$$
$$0=(2x+1)(2x-1)$$
$$2x+1=0$$
$$2x=-1$$
$$x=-\frac{1}{2}$$
$$2x-1=0$$
$$2x=1$$
$$x=\frac{1}{2}$$
Thus, the solution is $x=-\frac{1}{2},\frac{1}{2}$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
