Answer
(a) The graph of the equation $y=x^2-5x-24$ is as shown.
(b) The $x$-intercepts from the graph are $(-3,0)$ and $(8,0)$.
(c) The solution is $x=-3,8$.
(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 $y=x^2-5x-24$ is as shown.
(b) The $x$-intercepts from the graph are $(-3,0)$ and $(8,0)$.
(c) Setting $y=0$:
$$0=x^2-5x-24$$
$$0=(x+3)(x-8)$$
$$x+3=0$$
$$x=-3$$
$$x-8=0$$
$$x=8$$
Thus, the solution is $x=-3,8$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
