Question

What is the equation of the axis of symmetry for the function shown below?

y-2=-(x+5)^2
A. x = -5
B. x = 5
C. y = 2
D. x = 2

Answer 1

The axis of symmetry goes through the vertex vertically.

Answer 2

This equation is in vertex form. Can you tell what the vertex is?

Answer 3

(5,-2)

Answer 4

Close!

(-5,2) actually.

Answer 5

Recall that vertex form is:
\[y-k = C(x-h)^2\]

Where (h,k) is the vertex.

Answer 6

So your version:

y-2=-(x+5)^2

Is equivalent to:

y - 2 = -1(x-(-5))^2

Therefore h = -5, and k = 2

So (-5,2) is the vertex.

Answer 7

Now, what is the equation of a line that is vertical (up and down) that goes through (-5,2)

Answer 8

y=2

Answer 9

y = 2 is a horizontal line that goes through the y axis at y = 2.

Answer 10

a vertical line has the form x = h where h is the point on the x axis that the line intersects.