Question 129057: I am in 9th grade and taking Algebra 1. We are now learning to solve quadratic equations by graphing them. I just don't understand. For example, if they say graph quadratic einequalities and shade the solution region how do I do that? It's confusing.
y ≥ x2 (x squared)
y > -2x2 (x squared)
y ≥ x2 – 2x + 1 (x squared)
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! For quadratic inequalities, you are basically making a U that will go on forever, splitting the graph into what is inside the U and what is outside the U. All points inside the U will make the inequality true, or all points inside the U will make the inequality false. If a point makes the inequality true, it should be shaded. If the point makes it false, it should not be shaded. So you need to figure out if the inside of the U gets shaded or the outside of the U. So for each inequality, graph it like a regular quadratic equation. If it is "less than" or "greater than", then make the graph a dotted U. If it is "less than or equal to" or greater than or equal to," then make it a regular solid U. Then take one random point with simple numbers (0,0) or (1,0) or (0,1) are usually good choices as long as they do not lie on the U. If that point makes the inequality true, shade the part of the graph containing that point. If that point makes it false, shade the other part of the graph.
For y ≥ x^2, graph y=x^2, a solid-lined parabola opening upward with its vertex at (0,0). Now test a simple point. Since (0,0) is on the parabola, pick a different point. Try (0,1), right above the vertex inside the U. The inequality is
y ≥ x^2 and we are using y=1 and x=0. So we get the inequality (1)≥(0)^2, or 1≥0. This is a true statement, so (0,1), along with everything inside the U, gets shaded. Notice that (1,0), which lies outside the parabola, makes the inequality say 0≥1, which is false. That is why (1,0) is not in the shaded region. Try a few other points in the inequality to see how it works. I am not going to do the other 2 examples because this is ridiculously long already, but I hope it has helped. Good luck!
|
|
|
