Finite Math Examples

Find the x and y Intercepts f(x)=2x^3-15x^2-144x
Step 1
Find the x-intercepts.
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Step 1.1
To find the x-intercept(s), substitute in for and solve for .
Step 1.2
Solve the equation.
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Step 1.2.1
Rewrite the equation as .
Step 1.2.2
Factor out of .
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Step 1.2.2.1
Factor out of .
Step 1.2.2.2
Factor out of .
Step 1.2.2.3
Factor out of .
Step 1.2.2.4
Factor out of .
Step 1.2.2.5
Factor out of .
Step 1.2.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.4
Set equal to .
Step 1.2.5
Set equal to and solve for .
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Step 1.2.5.1
Set equal to .
Step 1.2.5.2
Solve for .
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Step 1.2.5.2.1
Use the quadratic formula to find the solutions.
Step 1.2.5.2.2
Substitute the values , , and into the quadratic formula and solve for .
Step 1.2.5.2.3
Simplify.
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Step 1.2.5.2.3.1
Simplify the numerator.
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Step 1.2.5.2.3.1.1
Raise to the power of .
Step 1.2.5.2.3.1.2
Multiply .
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Step 1.2.5.2.3.1.2.1
Multiply by .
Step 1.2.5.2.3.1.2.2
Multiply by .
Step 1.2.5.2.3.1.3
Add and .
Step 1.2.5.2.3.1.4
Rewrite as .
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Step 1.2.5.2.3.1.4.1
Factor out of .
Step 1.2.5.2.3.1.4.2
Rewrite as .
Step 1.2.5.2.3.1.5
Pull terms out from under the radical.
Step 1.2.5.2.3.2
Multiply by .
Step 1.2.5.2.4
Simplify the expression to solve for the portion of the .
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Step 1.2.5.2.4.1
Simplify the numerator.
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Step 1.2.5.2.4.1.1
Raise to the power of .
Step 1.2.5.2.4.1.2
Multiply .
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Step 1.2.5.2.4.1.2.1
Multiply by .
Step 1.2.5.2.4.1.2.2
Multiply by .
Step 1.2.5.2.4.1.3
Add and .
Step 1.2.5.2.4.1.4
Rewrite as .
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Step 1.2.5.2.4.1.4.1
Factor out of .
Step 1.2.5.2.4.1.4.2
Rewrite as .
Step 1.2.5.2.4.1.5
Pull terms out from under the radical.
Step 1.2.5.2.4.2
Multiply by .
Step 1.2.5.2.4.3
Change the to .
Step 1.2.5.2.5
Simplify the expression to solve for the portion of the .
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Step 1.2.5.2.5.1
Simplify the numerator.
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Step 1.2.5.2.5.1.1
Raise to the power of .
Step 1.2.5.2.5.1.2
Multiply .
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Step 1.2.5.2.5.1.2.1
Multiply by .
Step 1.2.5.2.5.1.2.2
Multiply by .
Step 1.2.5.2.5.1.3
Add and .
Step 1.2.5.2.5.1.4
Rewrite as .
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Step 1.2.5.2.5.1.4.1
Factor out of .
Step 1.2.5.2.5.1.4.2
Rewrite as .
Step 1.2.5.2.5.1.5
Pull terms out from under the radical.
Step 1.2.5.2.5.2
Multiply by .
Step 1.2.5.2.5.3
Change the to .
Step 1.2.5.2.6
The final answer is the combination of both solutions.
Step 1.2.6
The final solution is all the values that make true.
Step 1.3
x-intercept(s) in point form.
x-intercept(s):
x-intercept(s):
Step 2
Find the y-intercepts.
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Step 2.1
To find the y-intercept(s), substitute in for and solve for .
Step 2.2
Solve the equation.
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Step 2.2.1
Remove parentheses.
Step 2.2.2
Remove parentheses.
Step 2.2.3
Remove parentheses.
Step 2.2.4
Simplify .
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Step 2.2.4.1
Simplify each term.
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Step 2.2.4.1.1
Raising to any positive power yields .
Step 2.2.4.1.2
Multiply by .
Step 2.2.4.1.3
Raising to any positive power yields .
Step 2.2.4.1.4
Multiply by .
Step 2.2.4.1.5
Multiply by .
Step 2.2.4.2
Simplify by adding numbers.
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Step 2.2.4.2.1
Add and .
Step 2.2.4.2.2
Add and .
Step 2.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 3
List the intersections.
x-intercept(s):
y-intercept(s):
Step 4