# Graph x+2=6(y-3)^2

Simplify .
Rewrite.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Find the properties of the given parabola.
Rewrite the equation in vertex form.
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens right.
Opens Right
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.
Multiply by .
Find the focus.
The focus of a parabola can be found by adding to the x-coordinate if the parabola opens left or right.
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 vertical line found by subtracting from the x-coordinate of the vertex if the parabola opens left or right.
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 Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
Convert to decimal.
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
Multiply by .
Convert to decimal.
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify the expression.
Multiply by .
Simplify each term.
Simplify the numerator.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Convert to decimal.
Substitute the value into . In this case, the point is .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Simplify the numerator.
Multiply by .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Convert to decimal.
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Graph x+2=6(y-3)^2