Algebra Examples

Find the Vertex y=3/4x^2
Step 1
Rewrite the equation in vertex form.
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Step 1.1
Combine and .
Step 1.2
Complete the square for .
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Step 1.2.1
Use the form , to find the values of , , and .
Step 1.2.2
Consider the vertex form of a parabola.
Step 1.2.3
Find the value of using the formula .
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Step 1.2.3.1
Substitute the values of and into the formula .
Step 1.2.3.2
Simplify the right side.
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Step 1.2.3.2.1
Cancel the common factor of and .
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Step 1.2.3.2.1.1
Factor out of .
Step 1.2.3.2.1.2
Cancel the common factors.
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Step 1.2.3.2.1.2.1
Cancel the common factor.
Step 1.2.3.2.1.2.2
Rewrite the expression.
Step 1.2.3.2.2
Multiply the numerator by the reciprocal of the denominator.
Step 1.2.3.2.3
Multiply by .
Step 1.2.4
Find the value of using the formula .
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Step 1.2.4.1
Substitute the values of , and into the formula .
Step 1.2.4.2
Simplify the right side.
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Step 1.2.4.2.1
Simplify each term.
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Step 1.2.4.2.1.1
Raising to any positive power yields .
Step 1.2.4.2.1.2
Combine and .
Step 1.2.4.2.1.3
Multiply by .
Step 1.2.4.2.1.4
Divide by .
Step 1.2.4.2.1.5
Divide by .
Step 1.2.4.2.1.6
Multiply by .
Step 1.2.4.2.2
Add and .
Step 1.2.5
Substitute the values of , , and into the vertex form .
Step 1.3
Set equal to the new right side.
Step 2
Use the vertex form, , to determine the values of , , and .
Step 3
Find the vertex .
Step 4