| Write an equation for the parabola whose vertex is at (2, 0) and passes through (1, 4). |
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Step 1 |
The
vertex of the parabola is at (2, 0) so h
= 2 and k = 0 . Since (1, 4) is a point on the graph of the parabola, let x = 1 and y = 4 . 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. 4 = a(1 - 2)^2 + 0 \quad \quad \quad Substitute 4 for y, 1 for x, 2 for h, and 0 for k. |
Step 2 |
Simplify
the expression . |
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4 = a(1) + 0 4 = a |
Step 3 |
Write
the equation in vertex form. |
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Show Me |
y = 4(x - 2)^2 + 0 |
Step 4 |
Check. A graph of \quad y = 4(x - 2)^2 \quad verifies that the parabola passes through the point (1, 4). |
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