Use the vertex form, , to determine the values of , , and .

Since the value of is negative, the parabola opens down.

Opens Down

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.

Multiply by .

Move the negative in front of the fraction.

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 Down

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Direction: Opens Down

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Multiply by .

Simplify by adding numbers.

Add and .

Subtract from .

The final answer is .

The value at is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raise to the power of .

Multiply by .

Multiply by .

Simplify by adding and subtracting.

Add and .

Subtract from .

The final answer is .

The value at is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raising to any positive power yields .

Multiply by .

Multiply by .

Simplify by adding zeros.

Add and .

Subtract from .

The final answer is .

The value at is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

One to any power is one.

Multiply by .

Multiply by .

Simplify by subtracting numbers.

Subtract from .

Subtract from .

The final answer is .

The value at is .

Graph the parabola using its properties and the selected points.

Graph the parabola using its properties and the selected points.

Direction: Opens Down

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Graph h(x)=-2(x+1)^2+1