CPM Homework Help : A2C Problem 8-130

Find the x- and y-intercepts of the graphs of each of the following equations. Homework Help ✎
1. y = 2x³ − 10x² − x
2. y + 2 = log₃(x − 1)

Hint (a):

Set x to 0 and solve for y to find the y-intercept(s).
Set y 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 = 2x³ − 10x² − x
0 = x(2x² − 10x² − 1)

Let y = 0 to find the x-intercept. Then factor and use the Zero Product Property and the Quadratic Formula.

Answer (a):

y-intercept: (0,0)

$x\text{-intercepts: } (0, 0)\text{ and }\left(\frac{5\pm3\sqrt{3}}{2},0\right)$

Hint (b):

See part (a).

Answer (b):

x-intercept: (10, 0)
no y-intercept