Question

Name the vertex of the graph of

y=x^2−2x−120
(1 point)
Responses

(-1, -121)
(-1, -121)

(121, 1)
(121, 1)

(-121, 1)
(-121, 1)

(1, -121)

Answer 1

To find the vertex of the quadratic function given by \( y = x^2 - 2x - 120 \), we can use the vertex formula. The x-coordinate of the vertex can be found using the formula:

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

where \( a \) is the coefficient of \( x^2 \) and \( b \) is the coefficient of \( x \).

In the equation \( y = x^2 - 2x - 120 \):
- \( a = 1 \)
- \( b = -2 \)

Substituting these values into the formula:

\[
x = -\frac{-2}{2 \cdot 1} = \frac{2}{2} = 1
\]

Next, we substitute \( x = 1 \) back into the original equation to find the y-coordinate of the vertex:

\[
y = (1)^2 - 2(1) - 120
\]
\[
y = 1 - 2 - 120
\]
\[
y = -1 - 120 = -121
\]

Thus, the vertex of the graph is \( (1, -121) \).

The correct response is:

**(1, -121)**