Practice Test 4, Section 3, Number 11 (No Calc)
I love this question because the fastest way to go involves almost no math. You just have to know a little bit about the shapes of lines and parabolas.
First, think about the parabola. Its equation is . From that we know it’s a parabola that opens up (the
term will be positive) and has
-intercepts at
and
. You should figure out its
-intercept, too, by plugging in zero for
:
Do a very rough drawing of that on your paper (forgive my MS Paint skillz, but your drawing can be sloppier than mine and still be plenty good enough):
Now do a rough drawing of the line. To do that, put it in slope-intercept form:
The important detail there is that the -intercept is
, which is above the parabola’s
-intercept of
, so you know the line will intersect the parabola twice. Like so: