Question

what are the x- and y-intercepts of y= (x+2)√x show work?

Answer 1

Solving for x intercepts
\(\bf you~set~y=0\) in the equation

Solving for y intercepts
\(\bf you~set~x=0\) in the equation

Answer 2

what would that give you though

Answer 3

Solving for y intercepts
\(\bf you~set~x=0\) in the equation that means \(\bf y= ((0)+2)\sqrt{(0)}\)
what would you get for y?

Answer 4

you would get 0

Answer 5

Yes, that means the y-intercept is?

Answer 6

i know that for the answer it would be (0,0) and (-2,0) for the x intercepts and (0,0) for the y i just need to know how to do it

Answer 7

Y intercept is (0,0)

Solving for x intercepts
\(\bf you~set~y=0\) that means
\(\bf 0=(x+2)(\sqrt{x})\)
\(\color{red}{(x+2)}=0\) and \(\color{blue}{(\sqrt{x})}=0\)
\(\color{red}{x=-2}\) and \(\color{blue}{x=0}\)
so the x intercept will lie on (-2,0) and (0,0)

Answer 8

what part that you need more clarification of?

Answer 9

i'll be glad to clarify

Answer 10

yes that makes sense. could you help me with another one?

Answer 11

Sure

Answer 12

how do you show that there is x-axis symmetry for x=√(9-y^2)

Answer 13

x=sqrt(9-y^2)

Answer 14

@Zale101

Answer 15

to test for symmetry for f(x), you change the input positive x to negative x so f(-x).

Answer 16

how would you do that

Answer 17

@Zale101

Answer 18

\(f(y)=\sqrt{(9-y^2)}\)

\(f(-y)=\sqrt{(9-(-y)^2)}\) y is square rooted, that indicates that y is positive no matter what number we put there. That means, \(f(-y)\) has the same function of \(f(y)\). If i were to reflect the graph about the y axis, it would still look the same as the original equation. The name of this symmetry is y axis symmetry.
For more proof, let's see the graph of the equation.