Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the vertex
Find the axis of symmetry
Rewrite in vertex form
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(9,−83)
Evaluate
y=x2−6x×39−2
Simplify
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Evaluate
x2−6x×39−2
Divide the terms
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Evaluate
39
Reduce the numbers
13
Calculate
3
x2−6x×3−2
Multiply the terms
x2−18x−2
y=x2−18x−2
Find the x-coordinate of the vertex by substituting a=1 and b=−18 into x = −2ab
x=−2×1−18
Solve the equation for x
x=9
Find the y-coordinate of the vertex by evaluating the function for x=9
y=92−18×9−2
Calculate
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Evaluate
92−18×9−2
Multiply the numbers
92−162−2
Evaluate the power
81−162−2
Subtract the numbers
−83
y=−83
Solution
(9,−83)
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
y=x2−6x39−2
Simplify the expression
y=x2−18x−2
To test if the graph of y=x2−18x−2 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=(−x)2−18(−x)−2
Simplify
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Evaluate
(−x)2−18(−x)−2
Multiply the numbers
(−x)2+18x−2
Rewrite the expression
x2+18x−2
−y=x2+18x−2
Change the signs both sides
y=−x2−18x+2
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−9)2=y+83
Evaluate
y=x2−6x×39−2
Simplify
More Steps
Evaluate
x2−6x×39−2
Divide the terms
More Steps
Evaluate
39
Reduce the numbers
13
Calculate
3
x2−6x×3−2
Multiply the terms
x2−18x−2
y=x2−18x−2
Swap the sides of the equation
x2−18x−2=y
Move the constant to the right-hand side and change its sign
x2−18x=y−(−2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−18x=y+2
To complete the square, the same value needs to be added to both sides
x2−18x+81=y+2+81
Use a2−2ab+b2=(a−b)2 to factor the expression
(x−9)2=y+2+81
Solution
(x−9)2=y+83
Show Solution
Solve the equation
Solve for x
Solve for y
x=9+83+yx=9−83+y
Evaluate
y=x2−6x×39−2
Simplify
More Steps
Evaluate
x2−6x×39−2
Divide the terms
More Steps
Evaluate
39
Reduce the numbers
13
Calculate
3
x2−6x×3−2
Multiply the terms
x2−18x−2
y=x2−18x−2
Swap the sides of the equation
x2−18x−2=y
Move the expression to the left side
x2−18x−2−y=0
Substitute a=1,b=−18 and c=−2−y into the quadratic formula x=2a−b±b2−4ac
x=218±(−18)2−4(−2−y)
Simplify the expression
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Evaluate
(−18)2−4(−2−y)
Multiply the terms
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Evaluate
4(−2−y)
Apply the distributive property
−4×2−4y
Multiply the numbers
−8−4y
(−18)2−(−8−4y)
Rewrite the expression
182−(−8−4y)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
182+8+4y
Evaluate the power
324+8+4y
Add the numbers
332+4y
x=218±332+4y
Simplify the radical expression
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Evaluate
332+4y
Factor the expression
4(83+y)
The root of a product is equal to the product of the roots of each factor
4×83+y
Evaluate the root
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Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
283+y
x=218±283+y
Separate the equation into 2 possible cases
x=218+283+yx=218−283+y
Simplify the expression
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Evaluate
x=218+283+y
Divide the terms
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Evaluate
218+283+y
Rewrite the expression
22(9+83+y)
Reduce the fraction
9+83+y
x=9+83+y
x=9+83+yx=218−283+y
Solution
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Evaluate
x=218−283+y
Divide the terms
More Steps
Evaluate
218−283+y
Rewrite the expression
22(9−83+y)
Reduce the fraction
9−83+y
x=9−83+y
x=9+83+yx=9−83+y
Show Solution
Rewrite the equation
r=2cos2(θ)sin(θ)+18cos(θ)−1+331cos2(θ)+18sin(2θ)r=2cos2(θ)sin(θ)+18cos(θ)+1+331cos2(θ)+18sin(2θ)
Evaluate
y=x2−6x×39−2
Simplify
More Steps
Evaluate
x2−6x×39−2
Divide the terms
More Steps
Evaluate
39
Reduce the numbers
13
Calculate
3
x2−6x×3−2
Multiply the terms
x2−18x−2
y=x2−18x−2
Move the expression to the left side
y−x2+18x=−2
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r−(cos(θ)×r)2+18cos(θ)×r=−2
Factor the expression
−cos2(θ)×r2+(sin(θ)+18cos(θ))r=−2
Subtract the terms
−cos2(θ)×r2+(sin(θ)+18cos(θ))r−(−2)=−2−(−2)
Evaluate
−cos2(θ)×r2+(sin(θ)+18cos(θ))r+2=0
Solve using the quadratic formula
r=−2cos2(θ)−sin(θ)−18cos(θ)±(sin(θ)+18cos(θ))2−4(−cos2(θ))×2
Simplify
r=−2cos2(θ)−sin(θ)−18cos(θ)±1+331cos2(θ)+18sin(2θ)
Separate the equation into 2 possible cases
r=−2cos2(θ)−sin(θ)−18cos(θ)+1+331cos2(θ)+18sin(2θ)r=−2cos2(θ)−sin(θ)−18cos(θ)−1+331cos2(θ)+18sin(2θ)
Use b−a=−ba=−ba to rewrite the fraction
r=2cos2(θ)sin(θ)+18cos(θ)−1+331cos2(θ)+18sin(2θ)r=−2cos2(θ)−sin(θ)−18cos(θ)−1+331cos2(θ)+18sin(2θ)
Solution
r=2cos2(θ)sin(θ)+18cos(θ)−1+331cos2(θ)+18sin(2θ)r=2cos2(θ)sin(θ)+18cos(θ)+1+331cos2(θ)+18sin(2θ)
Show Solution
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