Question

the graph of $g(x) = x^2 + 2$ is a translation of the graph of $f(x)$ by units. up down left right

Explanation:

Step1: Identify Parent Function

The parent function for quadratic graphs is \( f(x) = x^2 \), which has its vertex at \((0,0)\).

Step2: Analyze Transformation

The function \( g(x) = x^2 + 2 \) is of the form \( f(x) + k \), where \( k = 2 \). For vertical translations, \( f(x) + k \) shifts the graph of \( f(x) \) up by \( k \) units when \( k > 0 \). Here, \( k = 2 > 0 \), so it's a vertical shift up by 2 units.

Step3: Match with Options

The dropdown options for direction: "up" is correct. The number of units is 2.

Answer:

The first dropdown: up; The second box: 2