Question

the graph shows a parabola and its focus. write the equation of the parabola in vertex form.

Explanation:

Step1: Determine the vertex form of a parabola

The vertex form of a parabola that opens to the right or left is \(y^{2}=4p(x - h)\), where \((h,k)\) is the vertex.
From the graph, the vertex \((h,k)=(0,0)\).

Step2: Find the value of \(p\)

The focus of a parabola \(y^{2}=4p(x - h)\) is \((h + p,k)\).
From the graph, the focus is \((1,0)\), so \(h + p=1\). Since \(h = 0\), then \(p = 1\).

Step3: Substitute \(h\) and \(p\) into the vertex - form equation

Substitute \(h = 0\) and \(p = 1\) into \(y^{2}=4p(x - h)\).
We get \(y^{2}=4\times1\times(x - 0)\), which simplifies to \(y^{2}=4x\).

Answer:

\(y^{2}=4x\)