Question

The graphs below have the same shape. what is the equation o the red graph?

Answer 1

So the equation of the red graph is already given to us:
`f(x) = x^2`. I assume you meant the blue graph?

We can use the vertex form:
`y = a(x - h)^2+ k`, where
`(h,k)` is the vertex. (We can ignore
`a` because
`a` is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).

The vertex for
`g(x)` is at
`(-4, -2)` on the coordinate plane. (4 left, 2 down)

Plug into the vertex form:

`y = (x - (-4))^2 -2`

The double negative becomes a positive, and then you're done:

`y = (x + 4)^2-2`