Question

1. $f(x)=-2(x + 5)^2 - 3$

Explanation:

Assuming the problem is to find the vertex of the parabola \( f(x) = -2(x + 5)^2 - 3 \), we can use the vertex form of a quadratic function.

Step-by-Step Explanation:

The vertex form of a quadratic function is given by:
\[ f(x) = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.

In the given function \( f(x) = -2(x + 5)^2 - 3 \), we can rewrite the term \((x + 5)\) as \((x - (-5))\).

Step 1: Identify \( h \) and \( k \)

• Comparing \( f(x) = -2(x - (-5))^2 + (-3) \) with the vertex form \( f(x) = a(x - h)^2 + k \):
• \( h = -5 \)
• \( k = -3 \)

Step 2: Determine the vertex

The vertex \((h, k)\) is \((-5, -3)\).

Final Answer:

The vertex of the parabola \( f(x) = -2(x + 5)^2 - 3 \) is \(\boxed{(-5, -3)}\).

Answer:

Assuming the problem is to find the vertex of the parabola \( f(x) = -2(x + 5)^2 - 3 \), we can use the vertex form of a quadratic function.

Step-by-Step Explanation:

The vertex form of a quadratic function is given by:
\[ f(x) = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.

In the given function \( f(x) = -2(x + 5)^2 - 3 \), we can rewrite the term \((x + 5)\) as \((x - (-5))\).

Step 1: Identify \( h \) and \( k \)

• Comparing \( f(x) = -2(x - (-5))^2 + (-3) \) with the vertex form \( f(x) = a(x - h)^2 + k \):
• \( h = -5 \)
• \( k = -3 \)

Step 2: Determine the vertex

The vertex \((h, k)\) is \((-5, -3)\).

Final Answer:

The vertex of the parabola \( f(x) = -2(x + 5)^2 - 3 \) is \(\boxed{(-5, -3)}\).