SOLUTION: Find the equation of the quadratic function satisfying the given conditions. ​(​Hint: Determine values of​ a, h, and k that satisfy ​P(x)=​a(x-​h)^2+​k.) Express the
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Question 1191949: Find the equation of the quadratic function satisfying the given conditions. ​(​Hint: Determine values of​ a, h, and k that satisfy ​P(x)=​a(x-​h)^2+​k.) Express the answer in the form ​P(x)=ax^2+bx+c. Use a calculator to support the result.
Vertex: (-3,-5); through (5,123)
P(x)=
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
y=ax^2+bx+c
-5=9a-3b+c
123=25a+5b+c
subtract 2 from 1
-128=-16a-8b
or
2a+b=16, multiplying by -1, dividing by 8, and rearranging the terms.
also
y=a(x+3)^2-5
123=64a-5
64a=128
a=2
b=12
y=2x^2+12x+13, the 13 comes from 2(x+3)^2-5. The constant is 2*3^2-5
-
-5=9a-3b+c, a=2 b=12 c=13 checks
123=25a+5b+c same
P(x)=2x^2+12x+13,
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The answer is found more easily if you use the given hint.
The vertex form of the equation is
where (h,k) is the vertex and a is a constant that determines the "steepness" of the parabola. The vertex is given...
... and the constant a is quickly determined using the other given point.
The vertex form is
Then
ANSWER: P(x) = 2x^2+12x+13
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