# Graph y=3x^2

Graph y=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 .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
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 .
Find the value of using the formula .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Divide by .
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 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.
Multiply by .
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.
Raise to the power of .
Multiply by .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Raise to the power of .
Multiply by .
The value at is .
Replace the variable with in the expression.
Simplify the result.
One to any power is one.
Multiply by .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Raise to the power of .
Multiply by .
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 five hundred seventy-three million two hundred eighty thousand seventy-one

### Interesting facts

• 1573280071 has 8 divisors, whose sum is 1762692624
• The reverse of 1573280071 is 1700823751
• Previous prime number is 37

### Basic properties

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

### Name

Name one billion five hundred fifty-three million four hundred ninety-five thousand four hundred fifty-seven

### Interesting facts

• 1553495457 has 4 divisors, whose sum is 2071327280
• The reverse of 1553495457 is 7545943551
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 48
• Digital Root 3

### Name

Name one billion two hundred eighty-three million one hundred twenty-seven thousand nine hundred sixty-four

### Interesting facts

• 1283127964 has 16 divisors, whose sum is 2957453856
• The reverse of 1283127964 is 4697213821
• Previous prime number is 41

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7