How do you graph and label the vertex and axis of symmetry #y=-4x^2-1#?

1 Answer
Jun 23, 2018

Take the graph of #y=x^2#, reflect it over the y-axis, translate the graph 1 unit down, and stretch the graph by a scale factor of 4. Put numbers into the equation and plot them on the graph. You should get this:
graph{-4x^2-1 [-10, 10, -10, 1]}

Explanation:

We can find the vertex algebraically. The x-coordinate of the vertex is found by using #x=-b/(2a)#. However, there is no b-value. Notice how, in the standard form of a quadratic equation (#y=ax^2+bx+c#), no #bx# term exists. When this happens, we replace #b# with #0#. #0# divided by anything is still #0#, so our x-value is #0#.

To find our y-value, we take our x-value and plug it into our original equation:

#y=-4(0)^2-1#
#y=-1#

We now have our vertex, #(0,-1)#. What about our axis of symmetry? Well, the axis passes through the vertex and would have to be a vertical line in our case. Using these, we can say that our axis of symmetry is #x=0#.