Question

a quadratic function f(x) is hidden from view. you must find the maximum value of the function f(x). choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently. form: vertex form f(x) = -2(x + 1)^2 + 8 answer attempt 1 out of 2

Explanation:

Step1: Recall Vertex Form Properties

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. If \( a < 0 \), the parabola opens downward, so the vertex is the maximum point.

Step2: Identify \( a \), \( h \), \( k \)

For \( f(x) = -2(x + 1)^2 + 8 \), rewrite \( (x + 1) \) as \( (x - (-1)) \), so \( h = -1 \), \( k = 8 \), and \( a = -2 \). Since \( a = -2 < 0 \), the parabola opens downward, so the maximum value is at the vertex's \( y \)-coordinate, which is \( k \).

Answer:

The maximum value of \( f(x) \) is \( 8 \).