To draw the graph, recall that the axis of symmetry is the vertical line through the vertex. Since we know the vertex is ( 0,0), the axis of symmetry is the line x= 0. Let's plot the vertex, the given point (- 3,3), and the point symmetric across the axis of symmetry.
Finally, let's connect the three points with a smooth curve. Do not use a straightedge for this part!
Equation
Recall the vertex form of a quadratic equation.
y= a(x- h)^2+ k
In this form, a is the leading coefficient of the quadratic function and the point ( h, k) is the vertex. Since the vertex of our function is ( 0, 0), we know that h= 0 and k= 0. We can partially write the vertex form.
y= a(x- 0)^2+ 0 ⇔ y=ax^2
We are told that the point (- 3,3) is on the curve. To find the value of a, we can substitute this point for x and y in our partial equation.
We are ready to write the vertex form of the function.
y=1/3x^2
Parent Function Comparison
Consider the parent function y=x^2. We have a vertical stretch when x^2 is multiplied by a number whose absolute value is greater than one. If x^2 is multiplied by a number whose absolute value is less than one, a vertical compression will take place.
In the given exercise, y=x^2 is multiplied by 13. Therefore, the previous graph will be vertically compressed by a factor of 13.
