SOLUTION: A parabola has x-intercepts 3 and 7 and has vertex (5,2). Determine the equation of this parabola in vertex form.

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Question 1202229: A parabola has x-intercepts 3 and 7 and has vertex (5,2). Determine the equation of this parabola in vertex form.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You could start with y=a%28x-h%29%5E2%2Bc.
Vertex occurs at the x value in the exact middle of 3 and 7. You could do the rest...

y=a%28x-5%29%5E2%2B2; and remember, you were given the x intercept points.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Given the vertex (5,2), the equation in vertex form is of the form

y=a%28x-5%29%5E2%2B2

You can use either of the given x-intercepts to determine the value of the constant a.

0=a%287-5%29%5E2%2B2
0=4a%2B2
4a=-2
a=-1%2F2

ANSWER: y=%28-1%2F2%29%28x-5%29%5E2%2B2

When you get familiar with the equations of parabolas, you can determine the constant a without using formal algebra. In this example, the reasoning would go like this:

From the vertex to either x-intercept, the change in x is 2. If the function were simply y=x^2, then the corresponding change in y would be 2^2=4. But the corresponding change in y in this example is -2; and that means the constant a is -2/4 = -1/2.