Calculus Examples

Find the x and y Intercepts y=6x^4+8x^3
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 1.2.3
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 and solve for .
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Step 1.2.4.1
Set equal to .
Step 1.2.4.2
Solve for .
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Step 1.2.4.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.4.2.2
Simplify .
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Step 1.2.4.2.2.1
Rewrite as .
Step 1.2.4.2.2.2
Pull terms out from under the radical, assuming real numbers.
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
Subtract from both sides of the equation.
Step 1.2.5.2.2
Divide each term in by and simplify.
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Step 1.2.5.2.2.1
Divide each term in by .
Step 1.2.5.2.2.2
Simplify the left side.
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Step 1.2.5.2.2.2.1
Cancel the common factor of .
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Step 1.2.5.2.2.2.1.1
Cancel the common factor.
Step 1.2.5.2.2.2.1.2
Divide by .
Step 1.2.5.2.2.3
Simplify the right side.
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Step 1.2.5.2.2.3.1
Move the negative in front of the fraction.
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 2.2.4.2
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