Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.

Question

y, equals, minus, 2, x, squared, minus, 16, x, minus, 20
y=−2x
2
−16x−20

Answer 1

To find the coordinates of the vertex of the parabola given by the equation \( y = -2x^2 - 16x - 20 \), we can use the formula for the vertex of a parabola in standard form \( y = ax^2 + bx + c \). The x-coordinate of the vertex can be found using the formula:

\[ x = -\frac{b}{2a} \]

In this equation, \( a = -2 \) and \( b = -16 \). Let's calculate the x-coordinate of the vertex:

\[ x = -\frac{-16}{2 \cdot -2} = \frac{16}{-4} = -4 \]

Next, we substitute this value of \( x \) back into the original equation to find the y-coordinate of the vertex:

\[ y = -2(-4)^2 - 16(-4) - 20 \] \[ y = -2(16) + 64 - 20 \] \[ y = -32 + 64 - 20 \] \[ y = 32 - 20 = 12 \]

Thus, the coordinates of the vertex of the parabola are:

\[ \boxed{(-4, 12)} \]