CPM Homework Help : CCA2 Problem 7-132

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7-132.

Find the x- and y-intercepts of the graphs of each of the following equations.

$y = 2x^{3} − 10x^{2} − x$
Hint (a):
Set $x\ \text{to} \ 0$ and solve for $y$ to find the $y-$ intercept(s).
Set $y\ \text{to}\ 0$ and solve for $x$ to find the $x-$ intercept(s).
Step 1(a):
Let $x = 0$ to find the $y-$ intercept.
$y = 2(0)^3 − 10(0)^2 − (0)$
Step 2(a):
$0 = 2x^3 − 10x^2 − x$
$0 = x\left(2x^2 − 10x^2 − 1\right)$
Let $y = 0$ to find the $x-$ intercept. Then factor and use the Zero Product Property and the Quadratic Formula.
Answer (a):
$y-\text{intercept:} \left(0,0\right)$
$x\text{-intercepts: } (0, 0)\text{ and }\left(\frac{5\pm3\sqrt{3}}{2},0\right)$

$y + 2 = log_{3}\left(x − 1\right)$
Hint (b):
See part (a).
Answer (b):
$x-$ intercept: $\left(10, 0\right)$
no $y-$ intercept

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