Question

graph the following function by moving the green and blue dots (if necessary). y = \frac{1}{3}x^{2}

Explanation:

Step1: Find key - points

When \(x = 0\), \(y=\frac{1}{3}\times0^{2}=0\); when \(x = 3\), \(y=\frac{1}{3}\times3^{2}=3\); when \(x=- 3\), \(y=\frac{1}{3}\times(-3)^{2}=3\); when \(x = 6\), \(y=\frac{1}{3}\times6^{2}=12\); when \(x=-6\), \(y=\frac{1}{3}\times(-6)^{2}=12\).

Step2: Plot the points

Plot the points \((0,0)\), \((3,3)\), \((-3,3)\), \((6,12)\), \((-6,12)\) etc. on the coordinate - plane.

Step3: Draw the curve

Connect the points with a smooth curve. Since the function \(y = \frac{1}{3}x^{2}\) is a parabola opening upwards (because the coefficient of \(x^{2}\) is positive \(\frac{1}{3}>0\)).

Answer:

The graph is a parabola opening upwards with vertex at the origin \((0,0)\) passing through points like \((3,3)\), \((-3,3)\) etc.