Question

question what is the vertex of the translated quadratic equation? a quadratic function $f(x)=x^2$ is plotted on a graph. what is the vertex of its transformation $g(x)=x^2 - 9$. answer attempt 1 out of 2 additional solution no solution submit answer

Explanation:

Step1: Recall vertex form of quadratic

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For the parent function \( f(x)=x^2 \), it can be written as \( f(x) = 1(x - 0)^2 + 0 \), so its vertex is \((0, 0)\).

Step2: Analyze transformation for \( g(x) \)

The function \( g(x)=x^2 - 9 \) can be rewritten as \( g(x)=1(x - 0)^2 - 9 \). Comparing with the vertex form \( y = a(x - h)^2 + k \), we have \( h = 0 \) and \( k=-9 \).

Answer:

The vertex of \( g(x)=x^2 - 9 \) is \((0, -9)\)