Question

What is the equation in vertex form of the quadratic function with a vertex at (-1, -4) that goes through (1, 8)?

f) y = (x-1)^2 -4
g) y = (x+1)^2-4
h) y = 3(x-1)^2- 4
j) y = 3(x+1)^2 -4

Answer 1

y = 3(x+1)^2 - 4

Explanation:The general form of the equation of a quadratic function whose vertex is (h,k) and whose leading coefficient is a is:

y - k = a(x-h)^2, or

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

Substituting the coefficients of the vertex (-1, -4), we get:

y = a(x + 1)^2 - 4

Substituting the coordinates of the given point, (1,8), we get:

8 = a(1+1)^2 - 4, which simplifies to:

8 = a(2)^2 - 4, or

8 = 4a - 4. Then 4a = 12, and a = 3.

Thus, the desired equation is y = 3(x+1)^2 - 4 (answer j).