SOLUTION: The vertex of a quadratic function is (-5,-3) and the graph of the function contains the point (1,2). Is this enough information to determine the equation of the function? if so, g

Algebra ->  Graphs -> SOLUTION: The vertex of a quadratic function is (-5,-3) and the graph of the function contains the point (1,2). Is this enough information to determine the equation of the function? if so, g      Log On


   

Question 168083: The vertex of a quadratic function is (-5,-3) and the graph of the function contains the point (1,2). Is this enough information to determine the equation of the function? if so, give the equation of the function. if not explain why.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Given the vertex (-5,-3) at points (1,2):
We can solve the eqn. using the Vertex Form in Solving Quadratic:
f%28x%29=a%28x-h%29%5E2%2Bk
f%28x%29=a%28x-%28-5%29%29%5E2%2B%28-3%29
f%28x%29=a%28x%2B5%29%5E2-3
2=a%28x%5E2%2B10x%2B25%29-3
2=a%281%5E2%2B10%2A1%2B25%29-3
2=36a-3
2%2B3=36a
cross%2836%29a%2Fcross%2836%29=5%2F36 --->a=5%2F36
It follows the eqn:f%28x%29=%285%2F36%29x%5E2%2B%285%2F36%2910x%2B%285%2F36%29%2825%29
f%28x%29=%285%2F36%29x%5E2%2B%2850%2F36%29x%2B%28125%2F36%29-3
f%28x%29=%285%2F36%29x%5E2%2B%2825%2F18%29x%2B%28125-108%29%2F36
highlight%28f%28x%29=%285%2F36%29x%5E2%2B%2825%2F18%29x%2B%2817%2F36%29%29, ANSWER
See graph:
----> See vertex (-5,-3) with points (1,2)
Thank you,
Jojo