SOLUTION: What is the equation of the quadratic function with roots 0 and 2 and a vertex at (1,5)

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Question 622852: What is the equation of the quadratic function with roots 0 and 2 and a vertex at (1,5)
Answer by math-vortex(472) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there -
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One way to solve this problem is to write the equation in vertex form:
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y=a%28x-h%29%5E2%2Bk
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When a quadratic is in this form, the point (h,k) is the vertex of the parabola. We know that the vertex of the parabola is (h,k)=(1,5).
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Substitute those known values for h and k in the equation.
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y=a%28x-1%29%5E2%2B5
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We know that two roots of the quadratic are 0 and 2. Roots of a quadratic are points where the graph crosses the x-axis. Thus the points (0,0) and (2,0) are on the parabola.
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We can substitute one of these points for x and y in our equation. Then we can solve for a. Arbitrarily, I'll choose the point (0,0). Either point will work.
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y=a%28x-1%29%5E2%2B5
0=a%280-1%29%5E2%2B5
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Simplify and solve for a.
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0=a%28-1%29%5E2%2B5
0=a%2B5
a=-5
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The equation for this quadratic is
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y=-5%28x-1%29%5E2%2B5
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Feel free to email me if you have questions about this solution.
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Ms.Figgy
math.in.the.vortex@gmail.com