SOLUTION: find the quadratic function that indicate vertex (5,12) and passes through points (7,15)?

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Question 287759: find the quadratic function that indicate vertex (5,12) and passes through points (7,15)?
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Put the equation in the form
y+=+ax%5E2+%2B+bx+%2B+c
The x-coordinate of the vertex is at -b%2F%282a%29
given:
(1) -b%2F%282a%29+=+5
(2) 12+=+a%2A5%5E2+%2B+b%2A5+%2B+c
(3) 15+=+a%2A7%5E2+%2B+b%2A7+%2B+c
This is 3 equations and 3 unknowns, so it's solvable
(1) b+=+-10a
Subtract (2) from (3)
(3) 15+=+49a+%2B+7b+%2B+c
(2) -12+=+-25a++-+5b+-+c
3+=+24a+%2B+2b
And, by substitution,
3+=+24a+%2B+2%2A%28-10a%29
3+=+24a+-+20a
4a+=+3
a+=+3%2F4
and
b+=+-10a
b+=+-30%2F4
b+=+-15%2F2
and
(3) 15+=+49a+%2B+7b+%2B+c
15+=+49%2A%283%2F4%29+%2B+7%2A%28-15%2F2%29+%2B+c
15+=+147%2F4+-+105%2F2+%2B+c
I made a mistake somewhere after this,
hope I gave you a good start

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a = 3/4, b = -15/2, c = 123/4
y=ax^2+bx+c