Find the General Form

Question

Use the vertex
(h, k)
and a point on the graph
(x, y)
to find the general form of the equation of the quadratic function.
(h, k) = (−4, −1), (x, y) = (−6, 3)

Answer 1

Vertex form:

 

y = a(x-h)² + k

 

(h,k) = (-4,-1)  (given)

 

y = a(x-(-4))² + (-1)

y = a(x+4)² - 1

 

To find a, plug in the known point (-6,3):

 

y = a(x+4)² - 1

3 = a(-6+4)² - 1

 

Solve for a.  If you need to, multiply the final vertex form out and combine like-terms to put it into standard form.