Question

determine the standard form of an equation of the parabola subject to the given conditions. vertex: (0, 0); directrix: x = -2 the equation of the parabola in standard form is

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola with vertex \((h,k)\) and directrix \(x = h - p\) is \((y - k)^2=4p(x - h)\).

Step2: Identify the values of \(h\), \(k\), and \(p\)

Given vertex \((h,k)=(0,0)\) and directrix \(x=- 2\). Since the directrix is \(x=h - p\), substituting \(h = 0\) into \(x=h - p\), we get \(-2=0 - p\), so \(p = 2\).

Step3: Substitute \(h\), \(k\), and \(p\) into the standard - form equation

Substitute \(h = 0\), \(k = 0\), and \(p = 2\) into \((y - k)^2=4p(x - h)\). We have \((y-0)^2=4\times2\times(x - 0)\).

Answer:

\(y^{2}=8x\)