The expression y = -2(x + 3)^2 + 6 is equivalent to ax^2 + bx + c, where a < 0 and b < 0. What is the value of c?

After expanding the expression y = − 2 ( x + 3 ) 2 + 6 , we find that it simplifies to y = − 2 x 2 − 12 x − 12 . Therefore, the value of c is − 12 .
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Answered by Anonymous | 2025-07-04

To find the value of c in the expression y = − 2 ( x + 3 ) 2 + 6 when it is written in the form a x 2 + b x + c , follow these steps:

Expand the expression :
The given expression is y = − 2 ( x + 3 ) 2 + 6 . We start by expanding the squared term:
( x + 3 ) 2 = x 2 + 6 x + 9 .

Distribute the − 2 :
Apply the distributive property to − 2 ( x 2 + 6 x + 9 ) :
− 2 ( x 2 + 6 x + 9 ) = − 2 x 2 − 12 x − 18 .

Combine with the constant term :
Add the constant term from the original expression, which is 6 :
y = − 2 x 2 − 12 x − 18 + 6 .

Simplify :
Simplify the expression:
y = − 2 x 2 − 12 x − 12 .

Identify a , b , and c :
In the expression y = a x 2 + b x + c , a = − 2 , b = − 12 , and c = − 12 .


So, the value of c is − 12 .

Answered by RyanHarmon181 | 2025-07-06