Question

Graph y = -­4x2 ­- 2 and its inverse

Answer 1

The function and it's inverse are graphed in the attached diagram.

For  y -intercept is $x=0$. This implies

$y=-4(0)^2-2$

$y=0-2$

$y=-2$

For x-intercept, $y=0$, This means that,

$0=-4x^2-2$

$-\frac{1}{2}=x^2$

The above equation tells us that, the above equation has no real roots. Hence the graph has no x-intercept.

Also the value $a=-4<0$, tells us the graph is a maximum graph.

THE INVERSE OF y

$y=-4x^2-2$

Interchange x and y.

$x=-4y^2-2$

Make y the subject to obtain,

$y^{-1}=\pm \frac{\sqrt{-x-2}}{2}$.

for x<-2.

You can now find the intercepts, with some few points to graph the inverse.