# Graph x=y-y^2

Reorder and .
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 .
Cancel the common factor of and .
Rewrite as .
Move the negative in front of the fraction.
Find the value of using the formula .
Simplify each term.
One to any power is one.
Multiply by .
Move the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
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 negative, the parabola opens left.
Opens Left
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.
Cancel the common factor of and .
Rewrite as .
Move the negative in front of the fraction.
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 Left
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Left
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.
Simplify the numerator.
Multiply by .
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 .
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 .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Cancel the common factor of and .
Rewrite as .
Cancel the common factors.
Rewrite as .
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 the numerator.
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply by .
Subtract from .
Reduce the expression by cancelling the common factors.
Cancel the common factor of and .
Rewrite as .
Cancel the common factors.
Rewrite as .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
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 Left
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Graph x=y-y^2