Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the vertex
Find the axis of symmetry
Evaluate the derivative
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(0,0)
Evaluate
b=(4×πa)a
Simplify
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Evaluate
(4×πa)a
Remove the parentheses
4×πa×a
Multiply the terms
π4a×a
Multiply the terms
π4a×a
Multiply the terms
π4a2
b=π4a2
Write the quadratic function in standard form
b=π4×a2
Find the a-coordinate of the vertex by substituting a=π4 and b=0 into a = −2ab
a=−2×π40
Solve the equation for a
a=0
Find the y-coordinate of the vertex by evaluating the function for a=0
b=π4×02
Calculate
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Evaluate
π4×02
Calculate
π4×0
Any expression multiplied by 0 equals 0
0
b=0
Solution
(0,0)
Show Solution
Solve the equation
Solve for a
Solve for b
a=2πba=−2πb
Evaluate
b=(4×πa)a
Simplify
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Evaluate
(4×πa)a
Remove the parentheses
4×πa×a
Multiply the terms
π4a×a
Multiply the terms
π4a×a
Multiply the terms
π4a2
b=π4a2
Swap the sides of the equation
π4a2=b
Cross multiply
4a2=πb
Divide both sides
44a2=4πb
Divide the numbers
a2=4πb
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±4πb
Simplify the expression
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Evaluate
4πb
To take a root of a fraction,take the root of the numerator and denominator separately
4πb
Simplify the radical expression
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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
2πb
a=±2πb
Solution
a=2πba=−2πb
Show Solution
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