# Graph f(x)=-x^2

Graph f(x)=-x^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 .
Move the negative one from the denominator of .
Simplify the expression.
Rewrite as .
Multiply 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 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.
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 .
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 Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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### Name

Name one billion four hundred sixty-eight million one hundred ninety-seven thousand six hundred eighty-four

### Interesting facts

• 1468197684 has 32 divisors, whose sum is 4893992640
• The reverse of 1468197684 is 4867918641
• Previous prime number is 9

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 54
• Digital Root 9

### Name

Name two hundred seventy-four million seven hundred fifty thousand eight hundred eighty-five

### Interesting facts

• 274750885 has 8 divisors, whose sum is 332218656
• The reverse of 274750885 is 588057472
• Previous prime number is 131

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 46
• Digital Root 1

### Name

Name one billion four hundred ninety-seven million six hundred seventy-five thousand two hundred sixty-three

### Interesting facts

• 1497675263 has 4 divisors, whose sum is 1711628880
• The reverse of 1497675263 is 3625767941
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 50
• Digital Root 5