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) =
...

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 \(|a|\) means same shape).
Given \(f(x) = 2x^2\), so \(a = 2\). The vertex \((h,k)=(6,4)\).

Step2: Substitute values into vertex form

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

Answer:

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