Question

what is the vertex of the graph of $y = 2(x - 2)^2 + 4$?

a. $(2, -4)$

b. $(2, -2)$

c. $(-2, 4)$

d. $(2, 4)$

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Identify \(h\) and \(k\) from given equation

In the equation \( y = 2(x - 2)^2 + 4 \), comparing with \( y = a(x - h)^2 + k \), we have \( h = 2 \) and \( k = 4 \). So the vertex is \((2, 4)\).

Answer:

D. (2, 4)