Question

Identify the vertex of y=−10(x+15)2−18
𝑦
=
−
10
(
𝑥
+
15
)
2
−
18
.(1 point)
Responses

(−150,−18)
(
−
150
,
−
18
)
left parenthesis negative 150 comma negative 18 right parenthesis

(−10,−15)
(
−
10
,
−
15
)
left parenthesis negative 10 comma negative 15 right parenthesis

(−15,−18)
(
−
15
,
−
18
)
left parenthesis negative 15 comma negative 18 right parenthesis

(15,−18)
(
15
,
−
18
)
left parenthesis 15 comma negative 18 right parenthesis

Answer 1

To find the vertex of the quadratic function \( y = -10(x + 15)^2 - 18 \), we can use the vertex form of a quadratic equation, which is given as:

\[ y = a(x - h)^2 + k \]

where \( (h, k) \) is the vertex.

In your equation, \( y = -10(x + 15)^2 - 18 \), we can rewrite the equation in the vertex form:

- Here, \( a = -10 \) (which determines the direction of the parabola),
- \( h = -15 \) (the value that makes the expression inside the parentheses zero),
- \( k = -18 \) (the constant term added).

Thus, the vertex is:

\[ (h, k) = (-15, -18) \]

So the correct answer from your options is:

**(−15,−18)**