Question

Give the equation of the axis of symmetry and the coordinates of the vertex of the reflection of y = 2(x + 2)2 - 3 across the line y=x.

Answer 1

Vertex: (-3, -2)

Axis of symmetry: y = -2

Step-by-step explanation:

When we reflect across the line y = x, we use the following rule to find the new coordinates:

(x, y) ---> (y, x)

Therefore, if the equation that relates y and x is y = 2(x+2)²-3, then the equation that relates x and y will be:

x = 2(y+2)²-3

Where we interchange the variables x and y.

So, this last equation is a parabola that opens to the right.

The equation of a parabola that opens to the right has the following form:

`x=a(y-k)^2+h`

Where (h, k) is the vertex and y = k is the axis of symmetry.

So, for our equation:

x = 2(y+2)²-3

(-3, -2) is the vertex and y = -2 is the axis of symmetry.