SOLUTION: For the following​ problem, find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. Write the function in standard form. Ver

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: For the following​ problem, find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. Write the function in standard form. Ver      Log On


   

Question 1176762: For the following​ problem, find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. Write the function in standard form.
Vertex (2,3); passing through (1,6)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Vertex (2,3); passing through (1,6)

f%28x%29+=a%28x-h%29%5E2%2Bk where h and k are coordinates of the vertex

if vertex (2,3) => h=2 and k=3

f%28x%29+=a%28x-2%29%5E2%2B3

if the parabola passing through (1,6)
6+=a%281-2%29%5E2%2B3.........solve for a
6+=a%28-1%29%5E2%2B3
6-3+=a%2A1
a=3
and equation is:
f%28x%29+=3%28x-2%29%5E2%2B3