Question

determine the quadratic inequality which matches the given graph.
y ≤ -x² + 4x + 3
y < -x² + 4x + 3
y ≥ -x² + 4x + 3
y > -x² + 4x + 3

Explanation:

Step1: Analyze the line type

The graph has a solid line, which means the inequality includes equality. So we can eliminate the inequalities with strict - less than ($<$) or strict - greater than ($>$) signs.

Step2: Analyze the shaded region

The region below the parabola $y=-x^{2}+4x + 3$ is shaded. This implies that $y$ is less than or equal to the value of the quadratic function.

Answer:

$y\leq -x^{2}+4x + 3$