Final answer:
A student's question involves expanding a quadratic function to find an equivalent form. The equivalent function to f(x)=-4(x+7)^2-6 is f(x)=-4x^2-56x-202.
Step-by-step explanation:
The student is asking about finding an equivalent function to f(x) = -4(x+7)^2 - 6.
To do this, we need to expand the given function using algebraic methods.
First, expand the squared term: (x+7)^2 becomes x^2 + 14x + 49.
Then distribute the -4 to get -4x^2 - 56x - 196.
Finally, add the -6 to get the expanded form of the quadratic function:
f(x) = -4x^2 - 56x - 202.
Therefore, the equivalent function is the third option.
Complete Question:
Which function is equivalent to f(x)=-4(x+7)^2-6 ？
f(x)=-4x^2+190
f(x)=-4x^2-56x-172
f(x)=-4x^2+14x+43
f(x)=-4x^2-56x-202