Question

1. the graph of function g is a translation 3 units right and 7 units up of the graph of f(x) = x². write function g in vertex form.

Explanation:

Step1: Recall Vertex Form Translation

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For a translation of \( h \) units right (replace \( x \) with \( x - h \)) and \( k \) units up (add \( k \)) to \( f(x)=x^2 \) (which has vertex \((0,0)\)).

Step2: Apply Translations

Here, translation is 3 units right (\( h = 3 \)) and 7 units up (\( k = 7 \)). So substitute into vertex form: \( g(x)=(x - 3)^2 + 7 \).

Answer:

\( g(x)=(x - 3)^2 + 7 \)