Question

write an equation in vertex form of the parabola that has the same shape as the graph of f(x)=2x², but with (6,4) as the vertex.
g(x) = \square

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( g(x)=a(x - h)^2 + k \), where \((h,k)\) is the vertex and \(a\) determines the shape (same as \(f(x)\) if \(a\) is same).

Step2: Determine values of \(a\), \(h\), \(k\)

Given \(f(x) = 2x^2\), so \(a = 2\). The vertex is \((6,4)\), so \(h = 6\) and \(k = 4\).

Step3: Substitute values into vertex form

Substitute \(a = 2\), \(h = 6\), \(k = 4\) into \(g(x)=a(x - h)^2 + k\). We get \(g(x)=2(x - 6)^2+4\).

Answer:

\(g(x)=2(x - 6)^2 + 4\)