# Graph f(x)=x^2-3x-2

Graph f(x)=x^2-3x-2
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 .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
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 .
Subtract from .
Move the negative in front of the fraction.
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 positive, the parabola opens up.
Opens Up
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 .
Cancel the common factor.
Rewrite the expression.
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 Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Up
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.
One to any power is one.
Multiply by .
Simplify by subtracting numbers.
Subtract from .
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 .
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 .
Simplify by subtracting numbers.
Subtract from .
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 .
Simplify by subtracting numbers.
Subtract from .
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 Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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### Name

Name one billion four hundred seventy million eight hundred ninety thousand five hundred

### Interesting facts

• 1470890500 has 64 divisors, whose sum is 5718824208
• The reverse of 1470890500 is 0050980741
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 34
• Digital Root 7

### Name

Name two billion thirty-four million six hundred sixty-five thousand one hundred sixty-five

### Interesting facts

• 2034665165 has 16 divisors, whose sum is 2632567728
• The reverse of 2034665165 is 5615664302
• Previous prime number is 853

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 38
• Digital Root 2

### Name

Name two billion nine million three hundred forty-seven thousand six hundred fifty-three

### Interesting facts

• 2009347653 has 8 divisors, whose sum is 2682739008
• The reverse of 2009347653 is 3567439002
• Previous prime number is 743

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 39
• Digital Root 3