Finite Math Examples

Find the x and y Intercepts f(x)=-5x^2+30x-50
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
Divide each term in by and simplify.
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Step 1.2.3.1
Divide each term in by .
Step 1.2.3.2
Simplify the left side.
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Step 1.2.3.2.1
Cancel the common factor of .
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Step 1.2.3.2.1.1
Cancel the common factor.
Step 1.2.3.2.1.2
Divide by .
Step 1.2.3.3
Simplify the right side.
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Step 1.2.3.3.1
Divide by .
Step 1.2.4
Use the quadratic formula to find the solutions.
Step 1.2.5
Substitute the values , , and into the quadratic formula and solve for .
Step 1.2.6
Simplify.
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Step 1.2.6.1
Simplify the numerator.
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Step 1.2.6.1.1
Raise to the power of .
Step 1.2.6.1.2
Multiply .
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Step 1.2.6.1.2.1
Multiply by .
Step 1.2.6.1.2.2
Multiply by .
Step 1.2.6.1.3
Subtract from .
Step 1.2.6.1.4
Rewrite as .
Step 1.2.6.1.5
Rewrite as .
Step 1.2.6.1.6
Rewrite as .
Step 1.2.6.1.7
Rewrite as .
Step 1.2.6.1.8
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.6.1.9
Move to the left of .
Step 1.2.6.2
Multiply by .
Step 1.2.6.3
Simplify .
Step 1.2.7
Simplify the expression to solve for the portion of the .
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Step 1.2.7.1
Simplify the numerator.
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Step 1.2.7.1.1
Raise to the power of .
Step 1.2.7.1.2
Multiply .
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Step 1.2.7.1.2.1
Multiply by .
Step 1.2.7.1.2.2
Multiply by .
Step 1.2.7.1.3
Subtract from .
Step 1.2.7.1.4
Rewrite as .
Step 1.2.7.1.5
Rewrite as .
Step 1.2.7.1.6
Rewrite as .
Step 1.2.7.1.7
Rewrite as .
Step 1.2.7.1.8
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.7.1.9
Move to the left of .
Step 1.2.7.2
Multiply by .
Step 1.2.7.3
Simplify .
Step 1.2.7.4
Change the to .
Step 1.2.8
Simplify the expression to solve for the portion of the .
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Step 1.2.8.1
Simplify the numerator.
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Step 1.2.8.1.1
Raise to the power of .
Step 1.2.8.1.2
Multiply .
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Step 1.2.8.1.2.1
Multiply by .
Step 1.2.8.1.2.2
Multiply by .
Step 1.2.8.1.3
Subtract from .
Step 1.2.8.1.4
Rewrite as .
Step 1.2.8.1.5
Rewrite as .
Step 1.2.8.1.6
Rewrite as .
Step 1.2.8.1.7
Rewrite as .
Step 1.2.8.1.8
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.8.1.9
Move to the left of .
Step 1.2.8.2
Multiply by .
Step 1.2.8.3
Simplify .
Step 1.2.8.4
Change the to .
Step 1.2.9
The final answer is the combination of both solutions.
Step 1.3
To find the x-intercept(s), substitute in for and solve for .
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
Raising to any positive power yields .
Step 2.2.3.1.2
Multiply by .
Step 2.2.3.1.3
Multiply by .
Step 2.2.3.2
Simplify by adding and subtracting.
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Step 2.2.3.2.1
Add and .
Step 2.2.3.2.2
Subtract from .
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