| Write an equation for the parabola whose vertex is at (6, 1) and passes through (5, 10). |
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Step 1 |
The
vertex of the parabola is at (6, 1) so h
= 6 and k = 1 . Since (5, 10) is a point on the graph of the parabola, let x = 5 and y = 10. Substitute these values into the vertex form of the equation and solve for a. |
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y = a(x - h)^2 + k \quad \quad Vertex
Form. 10 = a(5 - 6)^2 + 1 \quad \quad \quad Substitute 10 for y, 5 for x, 6 for h, and 1 for k. |
Step 2 |
Simplify
the expression . |
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Show Me |
10 = a(1) + 1 |
Step 3 |
Subtract
1 from each side . |
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Show Me |
9 = a(1) 9 = a |
Step 4 |
Divide
each side by 9 . |
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Show Me |
-\frac{1}{3} = a |
Step 5 |
Write
the equation in vertex form. |
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Show Me |
y = 9(x - 6)^2 + 1 |
Step 6 |
Check. A graph of \quad y = 9(x - 6)^2 + 1 \quad verifies that the parabola passes through the point (2, 1). |
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