SOLUTION: If been trying to find an equation for a vertex of (1,5) with x-intercepts of -5 and 7

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Question 812727: If been trying to find an equation for a vertex of (1,5) with x-intercepts of -5 and 7
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Parabola for simplicity, y=a%28x-h%29%5E2%2Bk standard form.

Vertex means, y=a%28x-1%29%5E2%2B5
If you make no assumptions about "a", try the given two intercepts in the equation:

0=a(-5-1)^2+5
-6a+5=0
-6a=-5
a=5/6

a%287-1%29%5E2%2B5=0
6a%2B5=0
6a=-5
a=-5%2F6---------we will want THIS, because:

....Thinking carefully about how the graph should appear, vertex (1,5) must be a maximum because it is above the two x-intercepts, so a%3C0 and we must choose a=-5%2F6

Our equation, parabola in standard form be highlight%28y=-%285%2F6%29%28x-1%29%5E2%2B5%29