SOLUTION: Write the equation of the quadratic function with vertex (-1,4) that contains (2,7).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Write the equation of the quadratic function with vertex (-1,4) that contains (2,7).       Log On


   

Question 672681: Write the equation of the quadratic function with vertex (-1,4) that contains (2,7).
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Vertex form of a quadratic equation: y=a%28x-h%29%5E2%2Bk
given: vertex (-1,4) that contains (2,7)
- Plug in the vertex and x and y coordinates of the point given, then solve for "a"
7=a%282-%28-1%29%29%5E2%2B4
7=a%282%2B1%29%5E2%2B4
7-4=a%283%29%5E2
3=9a
3%2F9=a
1%2F3=a
Now substitute "a" and the vertex into the vertex form:
y=%281%2F3%29%28x%2B1%29%5E2%2B4
y=%281%2F3%29%28x%5E2%2B2x%2B1%29%2B4
y=%281%2F3%29x%5E2%2B%282%2F3%29x%2B1%2F3%2B4
y=%281%2F3%29x%5E2%2B%282%2F3%29x%2B13%2F3