Find the Axis of Symmetry for the Quadratic Expression -5x^2 - 25x

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=-5x^2-25x$

To solve this problem, we'll follow these steps:

• Step 1: Identify the given coefficients $a$ and $b$.
• Step 2: Apply the formula for the axis of symmetry.
• Step 3: Perform the necessary calculations to find the axis of symmetry.

Now, let's work through each step:
Step 1: The given quadratic function is $f(x) = -5x^2 - 25x$, so $a = -5$ and $b = -25$.
Step 2: We'll use the axis of symmetry formula $x = -\frac{b}{2a}$.
Step 3: Plugging in our values, we get $x = -\frac{-25}{2 \times -5} = -\frac{25}{-10} = -2.5$.

Therefore, the axis of symmetry for the quadratic $f(x) = -5x^2 - 25x$ is $x = -2\frac{1}{2}$.