Question

the equation of the axis of symmetry of the following parabola algebraically
$y = -x^2 - 6x$

Explanation:

Step1: Recall the formula for the axis of symmetry of a parabola in the form \( y = ax^2 + bx + c \). The formula for the axis of symmetry is \( x = -\frac{b}{2a} \).

Step2: Identify the values of \( a \) and \( b \) from the given equation \( y = -x^2 - 6x \). Here, \( a = -1 \) and \( b = -6 \).

Step3: Substitute the values of \( a \) and \( b \) into the formula. So, \( x = -\frac{-6}{2\times(-1)} \).

Step4: Simplify the expression. First, calculate the numerator and the denominator. The numerator is \( -(-6) = 6 \), and the denominator is \( 2\times(-1) = -2 \). Then, \( x = \frac{6}{-2} = -3 \).

Answer:

The equation of the axis of symmetry is \( x = -3 \).