Question

mathematicians call this turning point the vertex
sketch a parabola whose vertex is on the y - axis.

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h,k)\) is the vertex. If the vertex is on the \(y\) - axis, then \(h = 0\). So the equation becomes \(y=ax^{2}+k\).

Step2: Choose values for \(a\) and \(k\)

Let's choose \(a = 1\) and \(k = 2\). Then the equation is \(y=x^{2}+2\).

Step3: Find some points to plot

When \(x = 0\), \(y=2\) (vertex). When \(x = 1\), \(y=1 + 2=3\). When \(x=- 1\), \(y=1 + 2 = 3\). When \(x = 2\), \(y=4 + 2=6\). When \(x=-2\), \(y=4 + 2=6\).

Answer:

Plot the points \((0,2)\), \((1,3)\), \((-1,3)\), \((2,6)\), \((-2,6)\) and connect them with a smooth curve. The resulting parabola \(y=x^{2}+2\) has its vertex \((0,2)\) on the \(y\) - axis.