Write the equation in vertex form for the parabola with focus (7,(15)/(4)) and directrix y=-(15)/(4).

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Identify Parabola Orientation: Identify whether the parabola is vertical or horizontal. Since the directrix is a horizontal line (y = constant), the parabola is vertical.Vertex Form of Vertical Parabola: Identify the vertex form of a vertical parabola. The vertex form of a vertical parabola is y = a(x-h)^2 + k, where (h,k) is the vertex.Determine Vertex: Determine the vertex of the parabola. The vertex lies midway between the focus and the directrix. Since the focus is at (7,15/4) and the directrix is y=-(15/4), the y-coordinate of the vertex will be the average of 15/4 and -15/4, which is 0. The x-coordinate of the vertex is the same as the x-coordinate of the focus, which is 7. Therefore, the vertex is at (7,0).Determine Parabola Direction: Determine if the parabola opens upward or downward. The focus is above the directrix, so the parabola opens upward.Calculate Value of 'a': Calculate the value of 'a'. The distance between the vertex and the focus (or directrix) is the absolute value of the difference in their y-coordinates. This distance is also equal to 1/(4a). The distance between the focus and the directrix is 15/4 - (-15/4) = 15/2. Therefore, 1/(4a) = 15/2, and a = 1/(4 * 15/2) = 1/(30).Write Parabola Equation: Write the equation of the parabola. Substitute a = 1/30, h = 7, and k = 0 into the vertex form equation. y = (1/30)(x-7)^2 + 0 y = (1/30)(x-7)^2

Write the equation in vertex form for the parabola with focus $\left(7, \frac{15}{4}\right)$ and directrix $y=-\frac{15}{4}$ .

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Write the equation in vertex form for the parabola with focus (7,154) \left(7, \frac{15}{4}\right) (7,415​) and directrix y=−154 y=-\frac{15}{4} y=−415​.

Write the equation in vertex form for the parabola with focus $\left(7, \frac{15}{4}\right)$ and directrix $y=-\frac{15}{4}$ .