Question

please help ASAP. Create a quadratic inequality that has this solution: x ≤ -7 or x ≥ -1. Explain your strategy.

Answer 1

Answer:   y ≤ x² + 8x + 7  

Step-by-step explanation:

x ≤ -7     --> x + 7 ≤ 0

x ≥ -1      --> x + 1 ≥ 0

• First, let's figure out the quadratic equation:

        y = (x + 7)(x + 1)

        y = x² + 8x + 7

• Next, let's figure out which inequality symbol to use:

        The quadratic is positive so it is U-shaped

        x ≤ -7    and    x ≥ -1    

       means the outside of the U-shaped parabola is shaded

        so we need to use the ≤ symbol

Note: if the inequality symbols were reversed, the shading would be inside the U-shaped parabola so we would use the ≥ symbol.