Finding Intercepts for y=x^2√(9-x^2)

[catteyes]

Homework Statement

y=x^2[SQ.RT.(9 - x^2)]

Homework Equations

The Attempt at a Solution

0= x^2 (+/- 3 - x)
0=x(x+3)(x-3)
x=0
x=3
x=-3



y=0[SQ.RT.(9-0)]
y=SQ.RT.(9)
y=+/-3
y= 3
y=-3

 

[rocomath]

This question should be posted in the Precalculus subforum.

Anyways, your question is find the x-int & y-int of $$y=x^2\sqrt{9-x^2}$$ correct?

Your procedure for finding the y-int are correct, but your work in finding the x-int is wrong.

You have $$\sqrt{9-x^2}$$ you cannot just take the square root, but your answers are right.

$$0=x^2\sqrt{9-x^2}$$

$$x^2=0$$
$$\sqrt{9-x^2}=0$$

 

[EnumaElish]

The X-axis intercepts are x=0, x=3, x=-3.

(Start with:

0 = x^2 sqrt[(x+3)(x-3)].

Hint: Square both sides.)

The Y-axis intercept(s) are easier to solve: the are found by substituting x = 0 into the formula.