Rewrite the equation as .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

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.

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

Find the value of using the formula .

Simplify each term.

Raising to any positive power yields .

Simplify the denominator.

Multiply by .

Combine and .

Reduce the expression by cancelling the common factors.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

Multiply by .

Add and .

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.

Simplify.

Cancel the common factor of and .

Rewrite as .

Move the negative in front of the fraction.

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

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 Left

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Direction: Opens Left

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

The final answer is .

Convert to decimal.

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

The final answer is .

Convert to decimal.

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

The final answer is .

Convert to decimal.

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

The final answer is .

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 y^2=-24x