Question

25 what are the coordinates of the vertex of the quadratic function whose equation is given? f(x) = 2(x + 1)² - 3 (-1, -3)

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Rewrite given function

Given \( f(x) = 2(x + 1)^2 - 3 \), rewrite \( (x + 1) \) as \( (x - (-1)) \). So the function becomes \( f(x) = 2(x - (-1))^2 + (-3) \).

Step3: Identify h and k

Comparing with \( f(x) = a(x - h)^2 + k \), we have \( h = -1 \) and \( k = -3 \).

Answer:

The coordinates of the vertex are \((-1, -3)\)