Question 514645
The y-intercept is the easy one, so let's start there.  The point where a function intersects the y-axis ALWAYS has an x-coordinate of 0 (to plot the point, you haven't moved left or right at all, you've only moved up or down).  Thus, to find the y-intercept, we can just plug in 0 for x.
{{{ f(x) = -X^2 + 5X + 24 }}}
{{{ f(0) = -(0)^2+5(0)+24}}}
{{{ f(0) = 24}}}
So, the y-intercept is the point (0, 24)


To find the x-intercept, we do the opposite and plug 0 in for y: {{{0=-x^2+5x+24}}}.  I hate having a negative in front of the {{{x^2}}} term, so let's divide everything by -1 (this will essentially change all the signs; 0 will still be 0 because 0 divided by -1 is still 0).
Now, we have {{{0=x^2-5x-24}}}.  This is factorable if we use -8 and 3 ({{{-8 + 3 = -5}}}, the middle term, and {{{-8 * 3 = -24}}}, the last term).  So it can be re-written as {{{0=(x-8)(x+3)}}}.


Recall that if two things multiply to 0, one of them must be 0 (for example, if {{{8 * x = 0}}}, then x=0).  Thus, either {{{x-8=0}}} or {{{x+3=0}}}.  If you solve each for x, you get x=8 or x=-3.  Those are the two solutions when y=0, so those are the two x-intercepts: (8, 0) and (-3, 0).