Calculus Examples

Find the x and y Intercepts x^4-6x^2
Step 1
Write as an equation.
Step 2
Find the x-intercepts.
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Step 2.1
To find the x-intercept(s), substitute in for and solve for .
Step 2.2
Solve the equation.
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Step 2.2.1
Rewrite the equation as .
Step 2.2.2
Factor the left side of the equation.
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Step 2.2.2.1
Rewrite as .
Step 2.2.2.2
Let . Substitute for all occurrences of .
Step 2.2.2.3
Factor out of .
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Step 2.2.2.3.1
Factor out of .
Step 2.2.2.3.2
Factor out of .
Step 2.2.2.3.3
Factor out of .
Step 2.2.2.4
Replace all occurrences of with .
Step 2.2.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.2.4
Set equal to and solve for .
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Step 2.2.4.1
Set equal to .
Step 2.2.4.2
Solve for .
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Step 2.2.4.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.2.4.2.2
Simplify .
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Step 2.2.4.2.2.1
Rewrite as .
Step 2.2.4.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.4.2.2.3
Plus or minus is .
Step 2.2.5
Set equal to and solve for .
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Step 2.2.5.1
Set equal to .
Step 2.2.5.2
Solve for .
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Step 2.2.5.2.1
Add to both sides of the equation.
Step 2.2.5.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.2.5.2.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.2.5.2.3.1
First, use the positive value of the to find the first solution.
Step 2.2.5.2.3.2
Next, use the negative value of the to find the second solution.
Step 2.2.5.2.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.2.6
The final solution is all the values that make true.
Step 2.3
x-intercept(s) in point form.
x-intercept(s):
x-intercept(s):
Step 3
Find the y-intercepts.
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Step 3.1
To find the y-intercept(s), substitute in for and solve for .
Step 3.2
Solve the equation.
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Step 3.2.1
Remove parentheses.
Step 3.2.2
Remove parentheses.
Step 3.2.3
Remove parentheses.
Step 3.2.4
Simplify .
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Step 3.2.4.1
Simplify each term.
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Step 3.2.4.1.1
Raising to any positive power yields .
Step 3.2.4.1.2
Raising to any positive power yields .
Step 3.2.4.1.3
Multiply by .
Step 3.2.4.2
Add and .
Step 3.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 4
List the intersections.
x-intercept(s):
y-intercept(s):
Step 5