Graph y=9-x^2

Math
Find the properties of the given parabola.
Tap for more steps…
Rewrite the equation in vertex form.
Tap for more steps…
Reorder and .
Complete the square for .
Tap for more steps…
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.
Tap for more steps…
Cancel the common factor of and .
Tap for more steps…
Factor out of .
Move the negative one from the denominator of .
Simplify the expression.
Tap for more steps…
Rewrite as .
Multiply by .
Find the value of using the formula .
Tap for more steps…
Simplify each term.
Tap for more steps…
Raising to any positive power yields .
Multiply by .
Divide by .
Multiply by .
Add and .
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.
Tap for more steps…
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 .
Tap for more steps…
Rewrite as .
Move the negative in front of the fraction.
Find the focus.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
Replace the variable with in the expression.
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Multiply by by adding the exponents.
Tap for more steps…
Multiply by .
Tap for more steps…
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raise to the power of .
Multiply by .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
One to any power is one.
Multiply by .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Raise to the power of .
Multiply by .
Add and .
The final answer is .
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:
Graph y=9-x^2

Do you need help with math?

Try our mobile app

Our app allows students to get instant step-by-step solutions to all kinds of math troubles.

Our MATH EXPERTS

JackHudson

Charlie Trom

Lucy Evel

Scroll to top