Question

A parabola opening up or down has vertex (3,-4) and passes through (-4,33/4).write it’s equation in vertex form

Answer 1

y = 1/4(x - 3)^2 - 4.

Explanation:

Vertex form is y = a(x - j)^2 + k where (j, k) is the vertex and a is some constant.

Here the vertex is (3 , -4) so we have:

y = a(x - 3)^2 - 4

Now we substitute the point x = -4 and y = 33/4 into the above:

33/4 = a(-4 - 3)^2 - 4

49a = 33/4 + 4 = 49/4

a = 49/4 / 49 = 1/4

So the parabola is 1/4(x - 3)^2 - 4.