Question

I need help with this problem
Graph y-2=-1/3(x+3)^2 and find the following
I have already made my graph and found the vertex, y-intercept, Max value, axis of symmetry. But I cant figure out how to calculate the x-intercept.

Answer 1

Vertex:-3,2
Max:2
Axis of Symmetry: -3
y-intercept: (0,-1)

Answer 2

the x-intercept means y = 0
so we can replace y with 0 in your equation to start with:
\[ y-2=-\frac{1}{3} (x+3)^2 \\ 0-2=-\frac{1}{3} (x+3)^2 \\ -2=-\frac{1}{3} (x+3)^2\]
I would multiply both sides by -3 to get
\[ -3 \cdot -2=-3 \cdot -\frac{1}{3}\cdot (x+3)^2 \\
6= (x+3)^2
\]
or
\[ (x+3)^2 = 6\]
I would take the square root of both sides as the next step.

Answer 3

Thank you, phi!