Find the equation of the axis of symmetry of the following parabola algebraically.

Question

y, equals, minus, 5, x, squared, minus, 20, x, minus, 40
y=−5x
2
−20x−40

Answer 1

To find the equation of the axis of symmetry for the parabola given by the equation $y=-5x^2-20x-40$, we can use the formula for the axis of symmetry given by $x=-\frac{b}{2a}$, where $a$ and $b$ are the coefficients from the standard quadratic form $y=a{x}^2+bx+c$.

In the equation $y=-5x^2-20x-40$:

• $a=-5$
• $b=-20$

Now we can substitute these values into the formula:

$$x=-\frac{b}{2a}=-\frac{-20}{2(-5)}=\frac{20}{-10}=-2$$

Thus, the equation of the axis of symmetry is:

$$x=-2$$