f y = (x + 3)2, then (-2x - 6)2 must equal which of the following?
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If y = (x + 3)^2, then (-2x - 6)^2 must equal which of the following?
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(x+3)^2 = fy
(-2x - 6)^2
= [-2(x+3)]^2
= (-2)^2 (x+3)^2
= 4 fy
To find the value of (-2x - 6)², we need to substitute this expression into the equation f(y) = (x + 3)² and solve for y.
Given: f(y) = (x + 3)²
We are given that y = (-2x - 6)²
Substituting the value of y into the equation, we have: f((-2x - 6)²) = [(x + 3)²]
To find the value of (-2x - 6)², we need to expand and simplify the expression.
(-2x - 6)² = (-2x - 6) * (-2x - 6) [Using the property (a + b)² = a² + 2ab + b²]
Expanding, we get: (-2x)(-2x) + (-2x)(-6) + (-6)(-2x) + (-6)(-6)
Simplifying, we have: 4x² + 12x + 12x + 36
Combining like terms, we get: 4x² + 24x + 36
Therefore, the expression (-2x - 6)² is equal to 4x² + 24x + 36.
Thus, the correct answer is "4x² + 24x + 36".