The vertex form of a parabola is given by the equation y = a(x-h)² + k, where (h,k) is the vertex of the parabola.

The vertex of the parabola is midway between the focus and the directrix. So, the y-coordinate of the vertex is the average of the y-coordinate of the focus and the y-coordinate of the directrix, which is (5+7)/2 = 6.

Since the focus is below the directrix, the parabola opens downwards. Therefore, the coefficient a is negative. The absolute value of a is 1/(4p), where p is the distance from the vertex to the focus (or to the directrix). In this case, p = 1, so a = -1/(4*1) = -1/4.

The x-coordinate of the vertex, focus and directrix are all 0, so h = 0.

Substituting h = 0, k = 6, and a = -1/4 into the vertex form equation gives:

y = -1/4(x - 0)² + 6
or
y = -1/4x² + 6

This is the equation of the parabola in vertex form.

Question

The vertex form of a parabola is given by the equation y = a(x-h)² + k, where (h,k) is the vertex of the parabola.

The vertex of the parabola is midway between the focus and the directrix. So, the y-coordinate of the vertex is the average of the y-coordinate of the focus and the y-coordinate of the directrix, which is (5+7)/2 = 6.

Since the focus is below the directrix, the parabola opens downwards. Therefore, the coefficient a is negative. The absolute value of a is 1/(4p), where p is the distance from the vertex to the focus (or to the directrix). In this case, p = 1, so a = -1/(4*1) = -1/4.

The x-coordinate of the vertex, focus and directrix are all 0, so h = 0.

Substituting h = 0, k = 6, and a = -1/4 into the vertex form equation gives:

y = -1/4(x - 0)² + 6
or
y = -1/4x² + 6

This is the equation of the parabola in vertex form.

Knowee AI · Accepted Answer

The vertex form of a parabola is given by the equation y = a(x-h)² + k, where (h,k) is the vertex of the parabola.

The vertex of the parabola is midway between the focus and the directrix. So, the y-coordinate of the vertex is the average of the y-coordinate of the focus and the y-coordinate of the directrix, which is (5+7)/2 = 6.

Since the focus is below the directrix, the parabola opens downwards. Therefore, the coefficient a is negative. The absolute value of a is 1/(4p), where p is the distance from the vertex to the focus (or to the directrix). In this case, p = 1, so a = -1/(4*1) = -1/4.

The x-coordinate of the vertex, focus and directrix are all 0, so h = 0.

Substituting h = 0, k = 6, and a = -1/4 into the vertex form equation gives:

y = -1/4(x - 0)² + 6
or
y = -1/4x² + 6

This is the equation of the parabola in vertex form.

orWatch a videoWrite the equation in vertex form for the parabola with focus (0,5) and directrix y=7.Simplify any fractions.

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