Sketch the curve of y=|15-4x-4x^2|

Question

Sketch the curve of y=|15-4x-4x^2|. If possible with detailed workings? Thanks

Answer 1

Since |y| = |-y|, you need to graph two parabolas:

 

y₁ = -4x² - 4x + 15            (vertex at (-1/2,16), zeros at -5/2 and 3/2, opens downward)

y₂ = -y₁ =  4x² + 4x -15     (vertex at (-1/2,-16). same zeros as above, opens upwards)

 

The graph of y = |-4x²-15x+15| will be the positive (y≥0, or parts above the x-axis) parts of the two graphs.  So in the interval [-5/2,3/2], it will be the graph of y₁; outside that interval, it will be the graph of y₂.  Click on the link below for the graph.

 

http://www.wyzant.com/resources/files/334201/graph_of_y_4x_2_4x_15