Question

25
write an equation of the parabola shown.
an equation of the parabola is

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens up or down is \((x - h)^2=4p(y - k)\), where \((h,k)\) is the vertex and \(p\) is the distance between the vertex and the directrix.

Step2: Identify the vertex and \(p\)

The vertex \((h,k)=(0,0)\). The directrix is \(y = - 8\). The distance \(p\) from the vertex \((0,0)\) to the directrix \(y=-8\) is \(p = 8\) (since the parabola opens upwards, \(p>0\)).

Step3: Substitute into the standard form

Substitute \(h = 0\), \(k = 0\), and \(p = 8\) into \((x - h)^2=4p(y - k)\). We get \(x^{2}=4\times8y\).

Answer:

\(x^{2}=32y\)