SOLUTION: Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h, k) = (−5, −1), (x, y) = (−7, 3

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h, k) = (−5, −1), (x, y) = (−7, 3      Log On


   

Question 1071429: Use the vertex (h, k)
and a point on the graph (x, y)
to find the general form of the equation of the quadratic function.
(h, k) = (−5, −1), (x, y) = (−7, 3)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Standard Form Equation for a Parabola:
y=a%28x-h%29%5E2%2Bk
for vertex (h,k)


What about the coefficient, a, in case you also have an included point on the parabola?

a%28x-h%29%5E2=y-k
highlight_green%28a=%28y-k%29%2F%28x-h%29%5E2%29-----and you would use your other given point to evaluate a. You were already also given (h,k) vertex.


Do you know what to do now?
( I did not substitute any values for you.)


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Student wants further help:
Substituting the values, this happens.
y=a%28x%2B5%29%5E2-1
solving for a and substituting the other point's values,
a=%283-%28-3%29%29%2F%28-7-%28-5%29%29%5E2=1
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Standard Form equation is y=%28x%2B5%29%5E2-1.
Fully multiply and further arithmetic simplification gives you general form y=x%5E2%2B10x%2B24.