SOLUTION: a quadratic graph has maximum point (2,5) and passes through point (0,-3). Find the equation for the graph in the form y=ax^2+bx+c

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a quadratic graph has maximum point (2,5) and passes through point (0,-3). Find the equation for the graph in the form y=ax^2+bx+c      Log On


   

Question 1125140: a quadratic graph has maximum point (2,5) and passes through point (0,-3). Find the equation for the graph in the form y=ax^2+bx+c
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the vertex form of the quadratic,
y=a%28x-h%29%5E2%2Bk
y=a%28x-2%29%5E2%2B5
Solve for a using the second point,
-3=a%280-2%29%5E2%2B5
-3=a%284%29%2B5
4a=-8
a=-2
So,
y=-2%28x-2%29%5E2%2B5
Expanding,
y=-2%28x%5E2-4x%2B4%29%2B5
y=-2x%5E2%2B8x-8%2B5
y=-2x%5E2%2B8x-3
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