Algebra
Calculus
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Question
Function
Evaluate the derivative
Find the domain
Find the x-intercept/zero
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y′={2x+52,x<32x−68,x>3
Evaluate
y=x2−8x−4∣x−3∣×15
Simplify
y=x2−8x−60∣x−3∣
Take the derivative of both sides
y′=dxd(x2−8x−60∣x−3∣)
Solution
y′={2x+52,x<32x−68,x>3
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=x2−8x−4∣x−3∣15
Simplify the expression
y=x2−8x−60∣x−3∣
To test if the graph of y=x2−8x−60∣x−3∣ is symmetry with respect to the origin,substitute -x for x and -y for y
−y=(−x)2−8(−x)−60∣−x−3∣
Simplify
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Evaluate
(−x)2−8(−x)−60∣−x−3∣
Calculate the absolute value
(−x)2−8(−x)−60∣x+3∣
Multiply the numbers
(−x)2+8x−60∣x+3∣
Rewrite the expression
x2+8x−60∣x+3∣
−y=x2+8x−60∣x+3∣
Change the signs both sides
y=−x2−8x+60∣x+3∣
Solution
Not symmetry with respect to the origin
Show Solution
Solve the equation
Solve for x
Solve for y
x∈(−∞,3)∩x=−26+856+y∪x∈(−∞,3)∩x=−26−856+y∪x∈[3,+∞)∩x=34+976+y∪x∈[3,+∞)∩x=34−976+y
Evaluate
y=x2−8x−4∣x−3∣×15
Simplify
y=x2−8x−60∣x−3∣
Swap the sides of the equation
x2−8x−60∣x−3∣=y
Move the expression to the left side
x2−8x−60∣x−3∣−y=0
Separate the equation into 2 possible cases
x2−8x−60(x−3)−y=0,x−3≥0x2−8x−60(−(x−3))−y=0,x−3<0
Solve the equation
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Evaluate
x2−8x−60(x−3)−y=0
Calculate
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Evaluate
x2−8x−60(x−3)−y
Expand the expression
x2−8x−60x+180−y
Subtract the terms
x2−68x+180−y
x2−68x+180−y=0
Substitute a=1,b=−68 and c=180−y into the quadratic formula x=2a−b±b2−4ac
x=268±(−68)2−4(180−y)
Simplify the expression
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Evaluate
(−68)2−4(180−y)
Multiply the terms
(−68)2−(720−4y)
Rewrite the expression
682−(720−4y)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
682−720+4y
Evaluate the power
4624−720+4y
Subtract the numbers
3904+4y
x=268±3904+4y
Simplify the radical expression
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Evaluate
3904+4y
Factor the expression
4(976+y)
The root of a product is equal to the product of the roots of each factor
4×976+y
Evaluate the root
2976+y
x=268±2976+y
Separate the equation into 2 possible cases
x=268+2976+yx=268−2976+y
Simplify the expression
x=34+976+yx=268−2976+y
Simplify the expression
x=34+976+yx=34−976+y
x=34+976+yx=34−976+y,x−3≥0x2−8x−60(−(x−3))−y=0,x−3<0
Solve the inequality
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Evaluate
x−3≥0
Move the constant to the right side
x≥0+3
Removing 0 doesn't change the value,so remove it from the expression
x≥3
x=34+976+yx=34−976+y,x≥3x2−8x−60(−(x−3))−y=0,x−3<0
Solve the equation
More Steps
Evaluate
x2−8x−60(−(x−3))−y=0
Calculate
x2−8x−60(−x+3)−y=0
Calculate
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Evaluate
x2−8x−60(−x+3)−y
Expand the expression
x2−8x+60x−180−y
Add the terms
x2+52x−180−y
x2+52x−180−y=0
Substitute a=1,b=52 and c=−180−y into the quadratic formula x=2a−b±b2−4ac
x=2−52±522−4(−180−y)
Simplify the expression
More Steps
Evaluate
522−4(−180−y)
Multiply the terms
522−(−720−4y)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
522+720+4y
Evaluate the power
2704+720+4y
Add the numbers
3424+4y
x=2−52±3424+4y
Simplify the radical expression
More Steps
Evaluate
3424+4y
Factor the expression
4(856+y)
The root of a product is equal to the product of the roots of each factor
4×856+y
Evaluate the root
2856+y
x=2−52±2856+y
Separate the equation into 2 possible cases
x=2−52+2856+yx=2−52−2856+y
Simplify the expression
x=−26+856+yx=2−52−2856+y
Simplify the expression
x=−26+856+yx=−26−856+y
x=34+976+yx=34−976+y,x≥3x=−26+856+yx=−26−856+y,x−3<0
Solve the inequality
More Steps
Evaluate
x−3<0
Move the constant to the right side
x<0+3
Removing 0 doesn't change the value,so remove it from the expression
x<3
x=34+976+yx=34−976+y,x≥3x=−26+856+yx=−26−856+y,x<3
Find the intersection
x∈[3,+∞)∩x=34+976+y∪x∈[3,+∞)∩x=34−976+yx=−26+856+yx=−26−856+y,x<3
Find the intersection
x∈[3,+∞)∩x=34+976+y∪x∈[3,+∞)∩x=34−976+yx∈(−∞,3)∩x=−26+856+y∪x∈(−∞,3)∩x=−26−856+y
Solution
x∈(−∞,3)∩x=−26+856+y∪x∈(−∞,3)∩x=−26−856+y∪x∈[3,+∞)∩x=34+976+y∪x∈[3,+∞)∩x=34−976+y
Show Solution
Graph
