Precalculus Examples

Find the X and Y Intercepts
To find the x-intercept, substitute in for and solve for .
Rewrite the equation as .
Move to the right side of the equation by subtracting from both sides of the equation.
Move to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
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Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Multiply by to get .
One to any power is one.
Set equal to and solve for .
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Set the factor equal to .
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Set equal to and solve for .
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Set the factor equal to .
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Move to the left side of the equation by adding it to both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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One to any power is one.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Rewrite as .
Rewrite as .
Rewrite as .
Multiply by to get .
Simplify the denominator.
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Rewrite.
Multiply by to get .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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One to any power is one.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Rewrite as .
Rewrite as .
Rewrite as .
Multiply by to get .
Simplify the denominator.
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Rewrite.
Multiply by to get .
-----Begin simplification-----
Rewrite as .
Factor out of .
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Factor out of .
Move .
Multiply by to get .
Factor out of .
Move the negative in front of the fraction.
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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One to any power is one.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Rewrite as .
Rewrite as .
Rewrite as .
Multiply by to get .
Simplify the denominator.
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Rewrite.
Multiply by to get .
-----Begin simplification-----
Rewrite as .
Move .
Factor out of .
Move the negative in front of the fraction.
The final answer is the combination of both solutions.
The solution is the result of and .
To find the y-intercept, substitute in for and solve for .
Solve the equation.
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Simplify each term.
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Remove parentheses around .
Raising to any positive power yields .
Subtract from to get .
These are the and intercepts of the equation .
x-intercept:
y-intercept:
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