SOLUTION: Find the quadratic function y​=f(x) whose graph has a vertex ​(-4​,4​) and passes through the point ​(-8​,0). Write the function in standard form.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the quadratic function y​=f(x) whose graph has a vertex ​(-4​,4​) and passes through the point ​(-8​,0). Write the function in standard form.      Log On


   

Question 1176572: Find the quadratic function y​=f(x) whose graph has a vertex ​(-4​,4​) and passes through the point ​(-8​,0). Write the function in standard form.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the quadratic is written in the form
y+=+a%28x-+h%29%5E2+%2B+k, then the vertex is the point (h, k%29%0D%0A%0D%0Aif+a+vertex+is+at++%E2%80%8B%28%7B%7B%7B-4​,4​), then h=-4 and k=4
y+=+a%28x-+%28-4%29%29%5E2+%2B+4
y+=+a%28x%2B4%29%5E2+%2B+4.........if passese through the point ​(-8%E2%80%8B,0), we have
0=+a%28-8%2B4%29%5E2+%2B+4........solve for a
0-4=+a%28-4%29%5E2+
-4=+a%2A16
a=-4%2F16
a=-1%2F4+
and your equation is:
y+=+-%281%2F4%29%28x%2B4%29%5E2+%2B+4