SOLUTION: Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. Vertex:(4, -1); point:(2,7)

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Question 946705: Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. Vertex:(4, -1); point:(2,7)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-h%29%5E2%2Bk
y-k=a%28x-h%29%5E2
a=%28y-k%29%2F%28x-h%29%5E2
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The vertex is (h,k);
Use the given point and the vertex coordinate values to compute a.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. Vertex:(4, -1); point:(2,7)
Vertex form of the equation of a parabola: y+=+a%28x+-+h%29%5E2+%2B+k

7+=+a%282+-+4%29%5E2+%2B+-+1 ------ Substituting (4, - 1) for (h, k), and (2, 7) for (x, y)

7 = a(4) - 1

7 + 1 = 4a

8 = 4a

a = 8%2F4, or 2

Vertex form of the equation of this parabola: y+=+2%28x+-+4%29%5E2+-+1

y+=+2%28x%5E2+-+8x+%2B+16%29+-+1

y+=+2x%5E2+-+16x+%2B+32+-+1

Standard form of the equation of this parabola: highlight_green%28y+=+2x%5E2+-+16x+%2B+31%29