Reflection across the x-axis and vertical stretch by a factor of 3.
We want to describe how the graph of the given quadratic function is related to the graph of its parent function f(x)=x^2. We will transform the graph of f(x)=x^2 to the graph of the given function.
g(x)=-3x^2
To do so, we need to consider two possible transformations.
Whenever x^2 is multiplied by a negative number, we will start by reflecting the graph across the x-axis.
Note how each x-coordinate stays the same, and how each y-coordinate changes its sign.
Stretch or Compression
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.
If x^2 is being multiplied by a negative number, the above still applies but everything will be upside down. In the given exercise, x^2 is multiplied by -3. Therefore, the graph of y=- x^2 will be vertically stretched by a factor of 3.
Final Graph
Let's now graph the given function and the parent function f(x)=x^2 on the same coordinate grid.
Finally, let's summarize how to draw the graph of the given function when starting with the graph of the parent function f(x)=x^2.
