Question

Which system is represented in the graph? y > x2 – 3x + 2y ≥ –x2 + 1 y < x2 – 3x + 2y < –x2 + 1 y ≥ x2 – 3x + 2y ≤ –x2 + 1 y > x2 – 3x + 2y < –x2 + 1

Answer 1

Explanation

To find the answer, we will have to find the equations that define the two functions

For the first graph

$\begin{gathered} let \\ f(x)=a(x+1)(x-1) \\ when\text{ } \\ x=0,\text{ y=1} \\ 1=a(1)(-1) \\ a=-1 \\ Thus \\ y\ge-1(x^2-1) \\ y\ge-x^2+1 \end{gathered}$

For the second graph (The purple)

$\begin{gathered} g(x)=a(x-1)(x-2) \\ when\text{ x=0,y=2} \\ 2=a(0-1)(0-2) \\ a=\frac{2}{-1\times-2}=\frac{2}{2}=1 \\ \\ a=1 \\ Thus,\text{ we have} \\ g(x)>1(x-1)(x-2) \\ g(x)>x^2-3x+2 \\ y>x^2-3x+2 \end{gathered}$

Thus, the answer is

$\begin{gathered} y\ge-x^2+1 \\ y>x^2-3x+2 \end{gathered}$