SOLUTION: What is the equation of the quadratic function that has a minimum at (7,-3) and goes through (9,9)?

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Question 1162223: What is the equation of the quadratic function that has a minimum at (7,-3) and goes through (9,9)?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The minimum point of a quadratic formula is the vertex.

y+=+Ax%5E2+%2B+Bx+%2B+C

Use vertex formula:

-B%2F%282A%29+=+7
-B=14A
B=-14A

Substitute in

y+=+Ax%5E2+%2B+Bx+%2B+C
y+=+Ax%5E2+%2B+%28-14A%29x+%2B+C
y+=+Ax%5E2-14Ax%2BC

Substitute (x,y) = (7,-3)

-3+=+A%287%29%5E2-14A%287%29%2BC

-3+=+49A-98A%2BC

-3+=+-49A%2BC

Substitute (x,y) = (9,9)

9+=+A%289%29%5E2-14A%289%29%2BC

9+=+81A-126A%2BC

9+=+-45A%2BC

system%28-3+=+-49A%2BC%2C9+=+-45A%2BC%29

Multiply the first equation by -1

system%283+=+49A-C%2C9+=+-45A%2BC%29 

Add the two equations term by term:

12=4A

3=A

B=-14A

B=-14%283%29

B=-42

3+=+49A-C
3+=+49%283%29-C
3+=+147-C
C=144


y+=+Ax%5E2+%2B+Bx+%2B+C
y+=+3x%5E2+-+42x%2B144

Edwin