Unit 4, Lesson 8
Cubes and Cube Roots
Algebra 2
8.1
Warm-up
How are these graphs the same? How are they different?
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How are these graphs the same? How are they different?
How many solutions are there to each of the following equations? Estimate the solution(s) from the graph of .
Check your estimate by substituting it back into the equation.
Every number has exactly one cube root. You can see this by looking at the graph of .
If is any number, for example, -4, then we can see that crosses the graph in one and only one place, so the equation will have the solution . This is true for any number : will cross the graph in exactly one place, and will have one solution, .
In an equation like , we can isolate the cube root, and then cube each side:
While cubing each side of an equation won’t create an equation with solutions that are different from the original equation, it is still a good idea to always check solutions in the original equation because little mistakes can creep in along the way.