Finite Math Examples

Find the x and y Intercepts y=6x-x^2
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 the left side of the equation.
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Step 1.2.2.1
Let . Substitute for all occurrences of .
Step 1.2.2.2
Factor out of .
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Step 1.2.2.2.1
Factor out of .
Step 1.2.2.2.2
Factor out of .
Step 1.2.2.2.3
Factor out of .
Step 1.2.2.3
Replace all occurrences of with .
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
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
Dividing two negative values results in a positive value.
Step 1.2.5.2.2.2.2
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
Divide by .
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
Simplify .
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Step 2.2.3.1
Simplify each term.
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Step 2.2.3.1.1
Multiply by .
Step 2.2.3.1.2
Raising to any positive power yields .
Step 2.2.3.1.3
Multiply by .
Step 2.2.3.2
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