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 \( y = ax^2 + bx + c \).

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:

\[ x = -2 \]