Question 1100203
The parent function is f(x) = x^2:<br>
{{{graph(400,400,-4,4,-50,20,x^2)}}}<br>
The graph is then reflected about the x-axis: f(x) = -x^2:<br>
{{{graph(400,400,-4,4,-50,20,-x^2)}}}<br>
Next the graph is stretched vertically  by a factor of 3: f(x) = -3x^2<br>
{{{graph(400,400,-4,4,-50,20,-3x^2)}}}<br>
Note those first two transformations can be done in either order; or they can be combined into a single transformation "reflect in the x-axis and stretch vertically by a factor of 3"<br>
Last the graph is translated down 5 units: f(x) = -3x^2-5:<br>
{{{graph(400,400,-4,4,-50,20,-3x^2-5)}}}<br>
It might be helpful to see the graphs of all the stages of the transformation on a single graph:<br>
{{{graph(400,400,-4,4,-50,20,x^2,-x^2,-3x^2,-3x^2-5)}}}<br>
red: parent graph, f(x) = x^2
green: reflected about the x-axis, f(x) = -x^2
blue: stretched by a vertical factor of 3, f(x) = -3x^2
purple: translated down 5 units, f(x) = -3x^2-5