Question

Write an equation in vertex form of the parabola that has the same shape as the graph of f(x)= 3x², but with the point (-7,4) as the vertex.

Answer 1

To write the equation of a parabola in vertex form, we use the following formula:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex of the new parabola is (-7,4), which means that h = -7 and k = 4. We also know that the shape of the parabola is the same as f(x) = 3x². Since the coefficient of x² is 3 in f(x), we need to multiply the entire equation by 3 to keep the same shape.

So the equation of the new parabola in vertex form is:

f(x) = 3(x + 7)^2 + 4

Note that we added 7 inside the parentheses to make sure that the vertex is at (-7, 4).