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

Question

.(1 point)
Responses

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

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

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

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

Answer 1

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

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

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

In this case, we can see that:

• \(a = -10\)
• The equation is of the form \(y = -10(x + 15)^2 - 18\), which means \(x + 15 = x - (-15)\); therefore, \(h = -15\).
• The value of \(k\) is \(-18\).

Thus, the vertex is located at (\(h, k\)) = \((-15, -18)\).

The correct response is:

\(\text{(−15, −18)}\)