Question

A system of inequalities is shown below

Which System is represented in the graph

Answer 1

`y > x^(2) -3x+2`

`y \ge -x^(2) +1`

Explanation:

The parabola opening downward has the equation
`y ? -x^(2) +1` , you can find this out by following a simple rule:

For a general equation:
`f(x) = ax^(2) +bx+c` if the leading coefficient a is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

Since we know which equation type belongs to which, we now find the exact equation:

So, to get the exact equation, we test points, for instance (3,0) is the solution region (blue area) of the graph. So we find the equation that gives us that solution. Which is
`y \ge -x^(2) +1`

The other equation, following the same rule is
`y > x^(2) -3x+2`