SOLUTION: Write a quadratic function in vertex form whose graph has the vertex (1,2) and passes through the point (3,10). (what does F(x)=?)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a quadratic function in vertex form whose graph has the vertex (1,2) and passes through the point (3,10). (what does F(x)=?)      Log On


   

Question 1030560: Write a quadratic function in vertex form whose graph has the vertex (1,2) and passes through the point (3,10).
(what does F(x)=?)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=f(x) or depending how you want to name the function, y=F(x).

y=a%28x-h%29%5E2%2Bk-------------generalized (NOT general) standard form, vertex (h,k).Your vertex is given.

y=a%28x-1%29%5E2%2B2

Use the known point on the quadratic function to determine coefficient a.
a%28x-1%29%5E2%2B2=y
a%28x-1%29%5E2=y-2
a=%28y-2%29%2F%28x-1%29%5E2
substitute the point.
a=%2810-2%29%2F%283-1%29%5E2
a=8%2F4
a=2---------------value of the coefficient found.

Final answer: highlight%28y=2%28x-1%29%5E2%2B2%29