Find a formula for the quadratic function whose graph has its vertex at (−1,4) and its y intercept at y = 0 .

Question

Find a formula for the quadratic function whose graph has its vertex at (−1,4) and its y-intercept at 𝑦=0

Answer 1

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

 

our given vertex of (-1,4) we have f(x) = a(x + 1)² +4.

 

Now we need to solve for a. To do so, we need to note that the y-intercept is 0. 

This means that f(0) = 0, because the y-intercept occurs where x = 0. 

 

Thus f(0) = a(0 + 1)² +4 = a +4.

 

0 = a +4

a=-4 

 .

 f(x) = -4(x + 1)² +4