Question

The graph of a quadratic function contains (4,-64) and it's vertex is at the origin.write an equation for this function.

Answer 1

Answer:

Step-by-step explanation:

Not sure what form you need this in, but it really doesn't matter, as you'll see in the final equation.  I used the vertex form and solved for a:

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

We are given the vertex (h, k) as the origin (0, 0), and we have a point that the graph goes through as (4, -64).  That's our x and y.  Plugging in what we have:

$-64=a(4-0)^2+0$ gives us

-64 = 16a and

a = -4.  That means that the quadratic equation is

$y=-4x^2$  which is both vertex form and standard form here, no difference.