Question

Use the graph of y ≤ 4x2 + 12x + 10 to determine which of the following points is a solution. The domain and range of the window is from -10 to 10.

http://prntscr.com/41qxfo

A. (-2, 0)
B. (-2, -1)
C. (0, 0)
D. (-1, 2)

Answer 1

Plug in the x-coordinate and check to see if the corresponding y-coordinate is less than or equal to the right side of the inequality.

For instance, take \((-2,0)\), then you have to check if the inequality holds:
\[y\overbrace{\le}^{\large?}4x^2+12x+10~~\iff~~0\overbrace{\le}^{\large?}4(-2)^2+12(-2)+10\]
The right side reduces to \(16-24+10=2\). Indeed, \(0\le2\), so \((-2,0)\) is a solution.

The graph you provided is actually the one for \(y\color{red}{\ge}4x^2+12x+10\), so make sure you have the right inequality in mind.