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Chapter 6: Problem 54

Find the standard form of the equation of the parabola with the given characteristics. Vertex: \((1,2) ;\) directrix: \(y=-1\)

Short Answer

Expert verified
The standard form of the equation of the parabola with the given characteristics is \(y = 1/12(x - 1)^2 + 2\).

Step by step solution

01

Find a

The formula for a is 1/(4d), where d is the distance between the vertex and the directrix. Since the vertex is (1,2) and the directrix is y=-1, the distance d is 2 -(-1) = 3. Therefore, \(a = 1/(4*3) = 1/12\).
02

Write the standard form of the parabola

Now that we have the value for a, we can substitute it into the standard form of a parabola. Since the parabola opens upwards (because a > 0), and the vertex is (1,2), the equation of the parabola is \(y = 1/12(x - 1)^2 + 2\).

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