Question

Name the vertex of the graph y=x2−2x−120
𝑦
=
𝑥
2
−
2
𝑥
−
120
(1 point)
Responses

(1,−121)
(
1
,
−
121
)
open paren 1 comma negative 121 close paren

(0,−120)
(
0
,
−
120
)
open paren 0 comma negative 120 close paren

(−10,0)
(
−
10
,
0
)
open paren negative 10 comma 0 close paren

(12,0)
(
12
,
0
)
open paren 12 comma 0 close paren
Question 2
Name the x-intercept(s) of the graph y=x2−2x−120
𝑦
=
𝑥
2
−
2
𝑥
−
120
(1 point)
Responses

(0,−120)
(
0
,
−
120
)
open paren 0 comma negative 120 close paren

(−1, −121)
(
−
1
,

−
121
)
(−1, −121)
(
−
1
,

−
121
)

(−10,0)(12,0)
(
−
10
,
0
)
(
12
,
0
)
open paren negative 10 comma 0 close paren times open paren 12 comma 0 close paren

(−12,0)(10,0)
(
−
12
,
0
)
(
10
,
0
)
open paren negative 12 comma 0 close paren times open paren 10 comma 0 close paren
Question 3
Name the y-intercept of the graph y=x2−2x−120
𝑦
=
𝑥
2
−
2
𝑥
−
120
(1 point)
Responses

(−10,0)
(
−
10
,
0
)
open paren negative 10 comma 0 close paren

(1,121)
(
1
,
121
)
open paren 1 comma 121 close paren

(1,−120)
(
1
,
−
120
)
open paren 1 comma negative 120 close paren

(1,−121)

Answer 1

To solve the given quadratic function \(y = x^2 - 2x - 120\), we can derive the answers for each question step by step.

### Question 1: Vertex of the Graph
The vertex of a parabola defined by the equation \(y = ax^2 + bx + c\) can be found using the formula:
\[
x = -\frac{b}{2a}
\]
For the equation \(y = x^2 - 2x - 120\):
- \(a = 1\)
- \(b = -2\)

Calculating the x-coordinate of the vertex:
\[
x = -\frac{-2}{2 \cdot 1} = \frac{2}{2} = 1
\]

To find the y-coordinate, substitute \(x = 1\) back into the equation:
\[
y = (1)^2 - 2(1) - 120 = 1 - 2 - 120 = -121
\]
Thus, the vertex is \((1, -121)\).

### Question 2: X-Intercept(s) of the Graph
The x-intercepts occur when \(y = 0\):
\[
0 = x^2 - 2x - 120
\]
We can factor this quadratic:
\[
0 = (x - 12)(x + 10)
\]

Setting each factor to zero gives the solutions:
\[
x - 12 = 0 \implies x = 12
\]
\[
x + 10 = 0 \implies x = -10
\]
Thus, the x-intercepts are \((-10, 0)\) and \((12, 0)\).

### Question 3: Y-Intercept of the Graph
The y-intercept occurs when \(x = 0\):
\[
y = 0^2 - 2(0) - 120 = -120
\]
Thus, the y-intercept is \((0, -120)\).

### Summary of Answers:
1. Vertex: \((1, -121)\)
2. X-Intercept(s): \((-10, 0)\) and \((12, 0)\)
3. Y-Intercept: \((0, -120)\)

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