Find the quadratic function that has a vertex at (-3,-1) and goes through the point (0,8)

Question

Find the quadratic function that has a vertex at (-3,-1) and goes through the point (0,8)

F(x)=

Answer 1

Hi Abraham,

We want to start with the vertex form of a quadratic function, which is:

f(x) = a(x - h)² + k , where point (h,k) is the vertex of the parabola.

Substituting our vertex, we get:

y = a(x + 3)² -1

We still need to find the coefficient a, so we substitute our given y-intercept (0,8) for x and y and solve for a:

8 = a(0 + 3)² - 1

8 = 9a - 1

9 = 9a

a = 1

Now we can write our final quadratic equation, starting again with vertex form:

f(x) = (x + 3)² - 1, or in standard quadratic form:

f(x) = x² + 6x + 8

Hope this helps!