Question
Function
Find the x-intercept/zero
Find the y-intercept
x1=−2−2,x2=−2+2
Evaluate
−9x2−36x−2y=18
To find the x-intercept,set y=0
−9x2−36x−2×0=18
Any expression multiplied by 0 equals 0
−9x2−36x−0=18
Removing 0 doesn't change the value,so remove it from the expression
−9x2−36x=18
Move the expression to the left side
−9x2−36x−18=0
Multiply both sides
9x2+36x+18=0
Substitute a=9,b=36 and c=18 into the quadratic formula x=2a−b±b2−4ac
x=2×9−36±362−4×9×18
Simplify the expression
x=18−36±362−4×9×18
Simplify the expression
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Evaluate
362−4×9×18
Multiply the terms
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Multiply the terms
4×9×18
Multiply the terms
36×18
Multiply the numbers
648
362−648
Evaluate the power
1296−648
Subtract the numbers
648
x=18−36±648
Simplify the radical expression
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Evaluate
648
Write the expression as a product where the root of one of the factors can be evaluated
324×2
Write the number in exponential form with the base of 18
182×2
The root of a product is equal to the product of the roots of each factor
182×2
Reduce the index of the radical and exponent with 2
182
x=18−36±182
Separate the equation into 2 possible cases
x=18−36+182x=18−36−182
Simplify the expression
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Evaluate
x=18−36+182
Divide the terms
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Evaluate
18−36+182
Rewrite the expression
1818(−2+2)
Reduce the fraction
−2+2
x=−2+2
x=−2+2x=18−36−182
Simplify the expression
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Evaluate
x=18−36−182
Divide the terms
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Evaluate
18−36−182
Rewrite the expression
1818(−2−2)
Reduce the fraction
−2−2
x=−2−2
x=−2+2x=−2−2
Solution
x1=−2−2,x2=−2+2
Show Solution

Solve the equation
Solve for x
Solve for y
x=3−6+18−2yx=−36+18−2y
Evaluate
−9x2−36x−2y=18
Move the expression to the left side
−9x2−36x−2y−18=0
Multiply both sides
9x2+36x+2y+18=0
Substitute a=9,b=36 and c=2y+18 into the quadratic formula x=2a−b±b2−4ac
x=2×9−36±362−4×9(2y+18)
Simplify the expression
x=18−36±362−4×9(2y+18)
Simplify the expression
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Evaluate
362−4×9(2y+18)
Multiply the terms
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Multiply the terms
4×9(2y+18)
Multiply the terms
36(2y+18)
Apply the distributive property
36×2y+36×18
Multiply the terms
72y+36×18
Multiply the numbers
72y+648
362−(72y+648)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
362−72y−648
Evaluate the power
1296−72y−648
Subtract the numbers
648−72y
x=18−36±648−72y
Simplify the radical expression
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Evaluate
648−72y
Factor the expression
72(9−y)
The root of a product is equal to the product of the roots of each factor
72×9−y
Evaluate the root
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Evaluate
72
Write the expression as a product where the root of one of the factors can be evaluated
36×2
Write the number in exponential form with the base of 6
62×2
The root of a product is equal to the product of the roots of each factor
62×2
Reduce the index of the radical and exponent with 2
62
62×9−y
Calculate the product
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Evaluate
2×9−y
The product of roots with the same index is equal to the root of the product
2(9−y)
Calculate the product
18−2y
618−2y
x=18−36±618−2y
Separate the equation into 2 possible cases
x=18−36+618−2yx=18−36−618−2y
Simplify the expression
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Evaluate
x=18−36+618−2y
Divide the terms
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Evaluate
18−36+618−2y
Rewrite the expression
186(−6+18−2y)
Cancel out the common factor 6
3−6+18−2y
x=3−6+18−2y
x=3−6+18−2yx=18−36−618−2y
Solution
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Evaluate
x=18−36−618−2y
Divide the terms
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Evaluate
18−36−618−2y
Rewrite the expression
186(−6−18−2y)
Cancel out the common factor 6
3−6−18−2y
Use b−a=−ba=−ba to rewrite the fraction
−36+18−2y
x=−36+18−2y
x=3−6+18−2yx=−36+18−2y
Show Solution

Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
−9x2−36x−2y=18
To test if the graph of −9x2−36x−2y=18 is symmetry with respect to the origin,substitute -x for x and -y for y
−9(−x)2−36(−x)−2(−y)=18
Evaluate
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Evaluate
−9(−x)2−36(−x)−2(−y)
Multiply the terms
−9x2−36(−x)−2(−y)
Multiply the numbers
−9x2+36x−2(−y)
Multiply the numbers
−9x2+36x+2y
−9x2+36x+2y=18
Solution
Not symmetry with respect to the origin
Show Solution

Identify the conic
Find the standard equation of the parabola
Find the vertex of the parabola
Find the focus of the parabola
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(x+2)2=−92(y−9)
Evaluate
−9x2−36x−2y=18
Move the expression to the right-hand side and change its sign
−9x2−36x=18−(−2y)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−9x2−36x=18+2y
Use the commutative property to reorder the terms
−9x2−36x=2y+18
Multiply both sides of the equation by −91
(−9x2−36x)(−91)=(2y+18)(−91)
Multiply the terms
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Evaluate
(−9x2−36x)(−91)
Use the the distributive property to expand the expression
−9x2(−91)−36x(−91)
Multiply the numbers
x2−36x(−91)
Multiply the numbers
x2+4x
x2+4x=(2y+18)(−91)
Multiply the terms
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Evaluate
(2y+18)(−91)
Apply the distributive property
2y(−91)+18(−91)
Multiply the numbers
−92y+18(−91)
Multiply the numbers
−92y−2
x2+4x=−92y−2
To complete the square, the same value needs to be added to both sides
x2+4x+4=−92y−2+4
Use a2+2ab+b2=(a+b)2 to factor the expression
(x+2)2=−92y−2+4
Add the numbers
(x+2)2=−92y+2
Solution
(x+2)2=−92(y−9)
Show Solution

Rewrite the equation
r=−9cos2(θ)18cos(θ)+sin(θ)+161cos2(θ)+18sin(2θ)+1r=9cos2(θ)−18cos(θ)−sin(θ)+161cos2(θ)+18sin(2θ)+1
Evaluate
−9x2−36x−2y=18
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
−9(cos(θ)×r)2−36cos(θ)×r−2sin(θ)×r=18
Factor the expression
−9cos2(θ)×r2+(−36cos(θ)−2sin(θ))r=18
Subtract the terms
−9cos2(θ)×r2+(−36cos(θ)−2sin(θ))r−18=18−18
Evaluate
−9cos2(θ)×r2+(−36cos(θ)−2sin(θ))r−18=0
Solve using the quadratic formula
r=−18cos2(θ)36cos(θ)+2sin(θ)±(−36cos(θ)−2sin(θ))2−4(−9cos2(θ))(−18)
Simplify
r=−18cos2(θ)36cos(θ)+2sin(θ)±644cos2(θ)+72sin(2θ)+4
Separate the equation into 2 possible cases
r=−18cos2(θ)36cos(θ)+2sin(θ)+644cos2(θ)+72sin(2θ)+4r=−18cos2(θ)36cos(θ)+2sin(θ)−644cos2(θ)+72sin(2θ)+4
Evaluate
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Evaluate
−18cos2(θ)36cos(θ)+2sin(θ)+644cos2(θ)+72sin(2θ)+4
Simplify the root
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Evaluate
644cos2(θ)+72sin(2θ)+4
Factor the expression
4(161cos2(θ)+18sin(2θ)+1)
Write the number in exponential form with the base of 2
22(161cos2(θ)+18sin(2θ)+1)
Calculate
2161cos2(θ)+18sin(2θ)+1
−18cos2(θ)36cos(θ)+2sin(θ)+2161cos2(θ)+18sin(2θ)+1
Use b−a=−ba=−ba to rewrite the fraction
−18cos2(θ)36cos(θ)+2sin(θ)+2161cos2(θ)+18sin(2θ)+1
Factor
−18cos2(θ)2(18cos(θ)+sin(θ)+161cos2(θ)+18sin(2θ)+1)
Reduce the fraction
−9cos2(θ)18cos(θ)+sin(θ)+161cos2(θ)+18sin(2θ)+1
r=−9cos2(θ)18cos(θ)+sin(θ)+161cos2(θ)+18sin(2θ)+1r=−18cos2(θ)36cos(θ)+2sin(θ)−644cos2(θ)+72sin(2θ)+4
Solution
More Steps

Evaluate
−18cos2(θ)36cos(θ)+2sin(θ)−644cos2(θ)+72sin(2θ)+4
Simplify the root
More Steps

Evaluate
644cos2(θ)+72sin(2θ)+4
Factor the expression
4(161cos2(θ)+18sin(2θ)+1)
Write the number in exponential form with the base of 2
22(161cos2(θ)+18sin(2θ)+1)
Calculate
2161cos2(θ)+18sin(2θ)+1
−18cos2(θ)36cos(θ)+2sin(θ)−2161cos2(θ)+18sin(2θ)+1
Use b−a=−ba=−ba to rewrite the fraction
−18cos2(θ)36cos(θ)+2sin(θ)−2161cos2(θ)+18sin(2θ)+1
Factor
−18cos2(θ)2(18cos(θ)+sin(θ)−161cos2(θ)+18sin(2θ)+1)
Reduce the fraction
−9cos2(θ)18cos(θ)+sin(θ)−161cos2(θ)+18sin(2θ)+1
Rewrite the expression
9cos2(θ)−18cos(θ)−sin(θ)+161cos2(θ)+18sin(2θ)+1
r=−9cos2(θ)18cos(θ)+sin(θ)+161cos2(θ)+18sin(2θ)+1r=9cos2(θ)−18cos(θ)−sin(θ)+161cos2(θ)+18sin(2θ)+1
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−9x−18
Calculate
−9x2−36x−2y=18
Take the derivative of both sides
dxd(−9x2−36x−2y)=dxd(18)
Calculate the derivative
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Evaluate
dxd(−9x2−36x−2y)
Use differentiation rules
dxd(−9x2)+dxd(−36x)+dxd(−2y)
Evaluate the derivative
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Evaluate
dxd(−9x2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−9×dxd(x2)
Use dxdxn=nxn−1 to find derivative
−9×2x
Multiply the terms
−18x
−18x+dxd(−36x)+dxd(−2y)
Evaluate the derivative
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Evaluate
dxd(−36x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−36×dxd(x)
Use dxdxn=nxn−1 to find derivative
−36×1
Any expression multiplied by 1 remains the same
−36
−18x−36+dxd(−2y)
Evaluate the derivative
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Evaluate
dxd(−2y)
Use differentiation rules
dyd(−2y)×dxdy
Evaluate the derivative
−2dxdy
−18x−36−2dxdy
−18x−36−2dxdy=dxd(18)
Calculate the derivative
−18x−36−2dxdy=0
Move the expression to the right-hand side and change its sign
−2dxdy=0+18x+36
Removing 0 doesn't change the value,so remove it from the expression
−2dxdy=18x+36
Change the signs on both sides of the equation
2dxdy=−18x−36
Divide both sides
22dxdy=2−18x−36
Divide the numbers
dxdy=2−18x−36
Solution
More Steps

Evaluate
2−18x−36
Rewrite the expression
22(−9x−18)
Reduce the fraction
−9x−18
dxdy=−9x−18
Show Solution
