SOLUTION: Determine the quadratic function f whose graph has the following, The vertex is (2,−1) and the other given point is (3,1) in form f(x) = ax^2+bx+c,

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine the quadratic function f whose graph has the following, The vertex is (2,−1) and the other given point is (3,1) in form f(x) = ax^2+bx+c,      Log On


   



Question 1074571: Determine the quadratic function f whose graph has the following,
The vertex is (2,−1) and the other given point is (3,1) in form f(x) = ax^2+bx+c,

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-2%29%5E2-1

y%2B1=a%28x-2%29%5E2
%28y%2B1%29%2F%28x-2%29%5E2=a
a=%281%2B1%29%2F%283-2%29%5E2
a=2

f(x)=2(x-2)^2-1
2%28x%5E2-4x%2B4%29-1
2x%5E2-8x%2B8-1
highlight%28f%28x%29=2x%5E2-8x%2B7%29

graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C2x%5E2-8x%2B7%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Determine the quadratic function f whose graph has the following,
The vertex is (2,−1) and the other given point is (3,1) in form f(x) = ax^2+bx+c,
f%28x%29+=+a%28x+-+h%29%5E2+%2B+k ------- Quadratic function, in vertex-form 
1+=+a%283+-+2%29%5E2+%2B+-+1 ------ Substituting (2, - 1) for (h, k), and (3, 1) for [x, f(x)]
1 = a - 1
1 + 1 = a
2 = a
f%28x%29+=+2%28x+-+2%29%5E2+-+1
f%28x%29+=+2%28x%5E2+-+4x+%2B+4%29+-+1
f%28x%29+=+2x%5E2+-+8x+%2B+8+-+1
Quadratic function: highlight_green%28matrix%281%2C3%2C+f%28x%29%2C+%22=%22%2C+2x%5E2+-+8x+%2B+7%29%29