To find the axis of symmetry for the given quadratic equation
[tex]\[
y = -5x^2 - 10x - 15,
\][/tex]
we use the standard formula for the axis of symmetry of a parabola, which is
[tex]\[
x = -\frac{b}{2a},
\][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are the coefficients from the quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex].
Here, the coefficients are:
- [tex]\( a = -5 \)[/tex]
- [tex]\( b = -10 \)[/tex]
Now substitute these values into the formula:
[tex]\[
x = -\frac{-10}{2 \cdot -5}
\][/tex]
Simplify the equation step-by-step:
[tex]\[
x = \frac{10}{-10}
\][/tex]
[tex]\[
x = -1
\][/tex]
Thus, the axis of symmetry for the given parabola is
[tex]\[
x = -1
\][/tex]
Therefore, written as an equation, the result is:
[tex]\[
x = -1.0
\][/tex]
