SOLUTION: Given Vertex (1,5) and Point (2,1) Write in vertex form & graph it. Please explain the steps too.

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Question 894040: Given Vertex (1,5) and Point (2,1) Write in vertex form & graph it. Please explain the steps too.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want a parabola? Should it open upward, downward, left, or right?

As a parabola, it could be parallel to the y-axis with a maximum for the vertex. This would mean that for standard y=a%28x-h%29%5E2%2Bk, a%3C0.

Solve for a.
a%28x-h%29%5E2=y-k
a=%28y-k%29%2F%28x-h%29%5E2;
Using the vertex coordinates,
a=%28y-5%29%2F%28x-1%29%5E2
Using also the given point on the parabola (as the shape I chose),
a=%281-5%29%2F%282-1%29%5E2
a=-4%2F1%5E2
a=-4
-
The equation can be highlight%28y=-4%28x-1%29%5E2%2B5%29.
You can use y=0 and find the x-axis intercepts.

graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C-4%28x-1%29%5E2%2B5%29