# Graph -x^2-3x-1

Graph -x^2-3x-1
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.
Multiply by .
Move the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
Find the value of using the formula .
Simplify 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 .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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 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.
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 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:
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.
Simplify the result.
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
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 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 .
Use the power rule to combine exponents.
Raise to the power of .
Multiply by .
Subtract from .
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 .
Subtract from .
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:
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### Name

Name one billion one hundred fifty-one million nine hundred fifty thousand four hundred fifty

### Interesting facts

• 1151950450 has 32 divisors, whose sum is 2074161024
• The reverse of 1151950450 is 0540591511
• Previous prime number is 101

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 31
• Digital Root 4

### Name

Name three hundred thirteen million thirty-three thousand seven hundred ninety-four

### Interesting facts

• 313033794 has 16 divisors, whose sum is 637880832
• The reverse of 313033794 is 497330313
• Previous prime number is 53

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 33
• Digital Root 6

### Name

Name five hundred fifty-nine million one hundred three thousand five hundred fifty-four

### Interesting facts

• 559103554 has 4 divisors, whose sum is 838655334
• The reverse of 559103554 is 455301955
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 37
• Digital Root 1