Mastery Check Solutions

Show What You Know

Graph.

$y < - 2 {(x - 5)}^{2} - 3 y \geq \frac{1}{2} \sqrt{x} - 6$

Note

Q: What are the types of inequalities being graphed?

A: A radical (square root) and a quadratic (parabola).

Remember that you can think about the transformations from the parent graphs to plot the inequalities.

Use the inequalities from part A to write transformed inequalities from the description below.
Transform the quadratic inequality up six spaces and left seven spaces from the given inequality. Transform the radical inequality up two spaces and multiply by a factor of four.

Quadratic:

$y < - 2 {(x - 5)}^{2} - 3 + 7 + 6 y < - 2 {(x + 2)}^{2} + 3$

Radical:

$y \geq \frac{1}{2} \sqrt{x} - 6 y \geq (4) \frac{1}{2} \sqrt{x} - 6 + 2 y \geq 2 \sqrt{x} - 4$

Describe the solution to the transformed system of inequalities.

When the graphs are transformed there will be no solution because the shaded regions no longer overlap.

Note

You do not need to graph the transformed inequalities, but you may want to draw a quick sketch to help determine where the shading will be.

Say What You Know

In your own words, talk about what you have learned using the objectives for this part of the lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

- Graph inequalities on the coordinate plane (absolute value, radical, linear, quadratic).
- Write an inequality given a graph.
- Determine the solutions for the graph of an inequality.