Answer:
The axis of symmetry for this parabola at x = -1
Step-by-step explanation:
y = -4x² - 8x - 7
We need to make a complete square to find the vertex of the parabola.
So,
y = -4x² - 8x - 7
= -4 ( x² + 2x ) - 7
= -4 ( x² + 2x + 1 - 1 ) - 7
= -4 ( x² + 2x + 1 ) + 4 - 7
y = -4 (x+1)² - 3
(y + 3) = -4 (x+1)²
Comparing the equation with the general form of the parabola:
y - k = a (x - h)²
where a is constant and (h,k) the vertex of the parabola.
So, the vertex of the given parabola is ( -1 , -3 )
So, the axis of symmetry for this parabola at x = -1
See the attached figure
