Identify the vertex of y=−10(x+15)2−18

Question

𝑦
=
−
10
(
𝑥
+
15
)
2
−
18
.(1 point)
Responses

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

(−150,−18)
(
−
150
,
−
18
)
left parenthesis negative 150 comma negative 18 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 given quadratic function \( y = -10(x + 15)^2 - 18 \), we can use the vertex form of a quadratic equation, which is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

In your equation:

• The term \( (x + 15)^2 \) can be rewritten as \( (x - (-15))^2 \). This tells us that \( h = -15 \).
• The constant term \(-18\) indicates that \( k = -18 \).

Thus, the vertex \((h, k)\) is:

\[ (-15, -18) \]

From the given options, the correct vertex is:

\[ \text{(−15,−18)} \]

So the final answer is:

\((−15,−18)\)