Question

Choose the graph of this quadratic inequality?

Answer 1

The answer is the first graph:

Explanation:

Given `y^2-x^2/9 >= 1`

We know that the equation:

`y^2-x^2/9 = 1`

Is a hyperbola with a vertical transverse axis; this eliminates graphs 3 and 4 because they have a horizontal transverse axis.

Because the inequality is greater than we choose the graph that has the yellow area above and below the hyperbola; this is graph 1.

Let's pretend that we cannot recognize the equations of a horizontal transverse axis hyperbola or a vertical transverse axis hyperbola and we do not know that the greater than relationship shades in above and below. How do we eliminate the graphs?

We let `x = 0`

`y^2-0^2/9 = 1`

`y^2= 1`

`y = +-1`

Please observe that the points `(0,1)` and (0,-1) are not in graphs 3 and 4; this eliminates them.

Please observe that the point `(0,0)` is in the yellow area of graph 2. Does `(0,0)` satisfy the equation:

`0^2-0^2/2 >=1`

`0 >= 1` NO!

Then it must be graph 1.