Algebra Examples

Find the x and y Intercepts y=x^2-2x+1
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 using the perfect square rule.
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Step 1.2.2.1
Rewrite as .
Step 1.2.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 1.2.2.3
Rewrite the polynomial.
Step 1.2.2.4
Factor using the perfect square trinomial rule , where and .
Step 1.2.3
Set the equal to .
Step 1.2.4
Add to both sides of the equation.
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
Raising to any positive power yields .
Step 2.2.3.1.2
Multiply by .
Step 2.2.3.2
Simplify by adding numbers.
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Step 2.2.3.2.1
Add and .
Step 2.2.3.2.2
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