# Algebra Examples

Arrange all the terms containing on the left side and all other terms on the right hand side.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.
Complete the square on the right side of the equation.
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Find the value of using the formula .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Multiply by to get .
Find the value of using the formula .
Simplify each term.
Simplify the numerator.
Remove parentheses around .
Raising to any positive power yields .
Simplify the denominator.
Remove parentheses.
Write as a fraction with denominator .
Multiply and to get .
Multiply the numerator by the reciprocal of the denominator.
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by to get .
Multiply by to get .
Substitute the values of , , and into the vertex form .
Reorder the right side of the equation to match the vertex form of a parabola.
Use the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens up.
Opens Up
Find the vertex .
Find , the distance from the vertex to the focus.
Find the distance from the vertex to a focus of the parabola by using the following formula.
Substitute the value of into the formula.
Simplify.
Simplify the denominator.
Multiply by to get .
Write as a fraction with denominator .
Multiply and to get .
Multiply the numerator by the reciprocal of the denominator.
Multiply by to get .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the focus.
The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Find the directrix.
The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.
Substitute the known values of and into the formula and simplify.
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:

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