# Graph minus x to the power of two minus three x minus one

Graph -x^2-3x-1
Calculate the properties of the given parabola.
Reformulate the equation as the vertex.
Complete the square for .
Consider the form, to find the values of , , and .
Consider the vertex form of a parabola.
Replace the values of and into the formula .
Clarify the right side.
First, First, multiply by .
Put the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
Find the value of using the formula .
Clarify each term.
Raise to the power of .
Multiply by .
Move the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Add numerators over the common denominator.
Clarify the numerator.
Multiply by .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Consider the vertex form, , to determine the values of , , and .
Since the value of is negative, the parabola opens down.
Opens Down
Find the vertex .
Calculate , 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.
The common factor should be canceled of and .
Should be rewritten as .
Move the negative in front of the fraction.
Calculate the focus.
The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Replace the known values of , , and into the formula and simplify.
Calculate the axis of symmetry by Calculateing the line that passes through the vertex and the focus.
Calculate 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.
Analyze and plot the parabola using its characteristics.
Direction: Opens Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Down
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.
Replace the variable with in the expression.
Clarify the result.
Clarify each term.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
The result 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 .
Subtract from .
The result is .
The value at is .
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 .
Apply the power rule to Add exponents.
Raise to the power of .
Multiply by .
Subtract from .
The result 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 .