Question

find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point. y = x² + 3

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.

Step2: Rewrite given equation

The given equation is \( y = x^2 + 3 \), which can be rewritten as \( y = 1(x - 0)^2 + 3 \).

Step3: Identify h and k

Comparing with \( y = a(x - h)^2 + k \), we have \( h = 0 \) and \( k = 3 \).

Answer:

\((0, 3)\)