SOLUTION: A parabola has vertex (3,-1) and an x intercept at (5,0). a). What is the other x intercept? I believe it to be (1,0) b). Find the equation of the parabola? This is what I am ha

Algebra ->  Equations -> SOLUTION: A parabola has vertex (3,-1) and an x intercept at (5,0). a). What is the other x intercept? I believe it to be (1,0) b). Find the equation of the parabola? This is what I am ha      Log On


   



Question 139103: A parabola has vertex (3,-1) and an x intercept at (5,0).
a). What is the other x intercept? I believe it to be (1,0)
b). Find the equation of the parabola? This is what I am having trouble figuring out.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola has vertex (3,-1) and an x intercept at (5,0).
a). What is the other x intercept? I believe it to be (1,0)
That would be true because of symmetry.
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b). Find the equation of the parabola? This is what I am having trouble figuring out.
Form: y-k = a(x-h)^2
Vertex: h= 3, k = -1
y+1 = a(x-3)^2
Using point x = 1 when y = 0 you can solve for "a":
1 = a(1-3)^2
1 = a(4)
a = 1/4
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EQUATION:
y = (1/4)(x-3)^2-1
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%281%2F4%29%28x-3%29%5E2-1%29
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Cheers,
Stan H.