# Graph y=-x^2

Graph y=-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 five hundred ninety-four million nine hundred eighty-eight thousand eight hundred ninety-five

### Interesting facts

• 594988895 has 16 divisors, whose sum is 761088000
• The reverse of 594988895 is 598889495
• Previous prime number is 79

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 65
• Digital Root 2

### Name

Name one billion nine hundred sixty-two million five hundred eighty-eight thousand thirty-six

### Interesting facts

• 1962588036 has 32 divisors, whose sum is 5987558880
• The reverse of 1962588036 is 6308852691
• Previous prime number is 59

### Basic properties

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

### Name

Name one billion four hundred sixty-five million one hundred seventy-one thousand one hundred twenty-one

### Interesting facts

• 1465171121 has 8 divisors, whose sum is 1535813664
• The reverse of 1465171121 is 1211715641
• Previous prime number is 41

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 29
• Digital Root 2