# Graph f(x)=x^2+14x+48

Graph f(x)=x^2+14x+48
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 .
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.
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 six hundred two million four hundred twenty-five thousand sixty-one

### Interesting facts

• 1602425061 has 8 divisors, whose sum is 2159540960
• The reverse of 1602425061 is 1605242061
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 27
• Digital Root 9

### Name

Name one billion four hundred ten million six hundred forty-seven thousand eight hundred sixty-eight

### Interesting facts

• 1410647868 has 64 divisors, whose sum is 3705730560
• The reverse of 1410647868 is 8687460141
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 45
• Digital Root 9

### Name

Name one billion four hundred ninety-five million eight hundred forty-five thousand three hundred forty

### Interesting facts

• 1495845340 has 32 divisors, whose sum is 4405945104
• The reverse of 1495845340 is 0435485941
• Previous prime number is 5

### Basic properties

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