Question
Function
Find the vertex
Find the axis of symmetry
Rewrite in vertex form
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(−34,3468)
Evaluate
s=−204t−3t2
Write the quadratic function in standard form
s=−3t2−204t
Find the t-coordinate of the vertex by substituting a=−3 and b=−204 into t = −2ab
t=−2(−3)−204
Solve the equation for t
t=−34
Find the y-coordinate of the vertex by evaluating the function for t=−34
s=−3(−34)2−204(−34)
Calculate
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Evaluate
−3(−34)2−204(−34)
Multiply the terms
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Evaluate
−3(−34)2
Evaluate the power
−3×1156
Multiply the numbers
−3468
−3468−204(−34)
Multiply the numbers
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Evaluate
204(−34)
Multiplying or dividing an odd number of negative terms equals a negative
−204×34
Multiply the numbers
−6936
−3468−(−6936)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−3468+6936
Add the numbers
3468
s=3468
Solution
(−34,3468)
Show Solution

Solve the equation
t=3−102+10404−3st=−3102+10404−3s
Evaluate
s=−204t−3t2
Swap the sides of the equation
−204t−3t2=s
Move the expression to the left side
−204t−3t2−s=0
Rewrite in standard form
−3t2−204t−s=0
Multiply both sides
3t2+204t+s=0
Substitute a=3,b=204 and c=s into the quadratic formula t=2a−b±b2−4ac
t=2×3−204±2042−4×3s
Simplify the expression
t=6−204±2042−4×3s
Simplify the expression
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Evaluate
2042−4×3s
Multiply the terms
2042−12s
Evaluate the power
41616−12s
t=6−204±41616−12s
Simplify the radical expression
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Evaluate
41616−12s
Factor the expression
12(3468−s)
The root of a product is equal to the product of the roots of each factor
12×3468−s
Evaluate the root
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Evaluate
12
Write the expression as a product where the root of one of the factors can be evaluated
4×3
Write the number in exponential form with the base of 2
22×3
The root of a product is equal to the product of the roots of each factor
22×3
Reduce the index of the radical and exponent with 2
23
23×3468−s
Calculate the product
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Evaluate
3×3468−s
The product of roots with the same index is equal to the root of the product
3(3468−s)
Calculate the product
10404−3s
210404−3s
t=6−204±210404−3s
Separate the equation into 2 possible cases
t=6−204+210404−3st=6−204−210404−3s
Simplify the expression
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Evaluate
t=6−204+210404−3s
Divide the terms
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Evaluate
6−204+210404−3s
Rewrite the expression
62(−102+10404−3s)
Cancel out the common factor 2
3−102+10404−3s
t=3−102+10404−3s
t=3−102+10404−3st=6−204−210404−3s
Solution
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Evaluate
t=6−204−210404−3s
Divide the terms
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Evaluate
6−204−210404−3s
Rewrite the expression
62(−102−10404−3s)
Cancel out the common factor 2
3−102−10404−3s
Use b−a=−ba=−ba to rewrite the fraction
−3102+10404−3s
t=−3102+10404−3s
t=3−102+10404−3st=−3102+10404−3s
Show Solution
