# Graph y=x^2-12x+2

Graph y=x^2-12x+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 .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
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.
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.
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.
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.
Raise to the power of .
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 Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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### Name

Name one billion three hundred twenty-four million two hundred seventeen thousand nine hundred fifty

### Interesting facts

• 1324217950 has 128 divisors, whose sum is 3477178368
• The reverse of 1324217950 is 0597124231
• Previous prime number is 47

### Basic properties

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

### Name

Name five hundred thirty-three million three hundred seventy-one thousand eight hundred seventy-eight

### Interesting facts

• 533371878 has 16 divisors, whose sum is 836790864
• The reverse of 533371878 is 878173335
• Previous prime number is 117

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 45
• Digital Root 9

### Name

Name one billion seven hundred eight million eight hundred seventy-one thousand six hundred six

### Interesting facts

• 1708871606 has 8 divisors, whose sum is 2760484944
• The reverse of 1708871606 is 6061788071
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8