Question

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

Answer 1

Answer:

Es pero que te ayude amigo

Answer 2

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:

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