Question

1. the graph of $y = (x - 2)^2 - 9$ can be obtained from the graph of $y = x^2$ by shifting horizontally ____ units to the __ and shifting vertically __ units to the ____ direction.

a) 2; right; 9; downward b) 9; right; 2; downward c) 2; left; 9; downward d) 2; left; 9; upward

Explanation:

Step1: Recall transformation rules

For a function \( y = f(x - h)+k \), horizontal shift: \( h \) units right if \( h>0 \), left if \( h < 0 \); vertical shift: \( k \) units up if \( k>0 \), down if \( k < 0 \).
Given \( y=(x - 2)^{2}-9 \) and \( y = x^{2}=f(x) \), here \( h = 2 \), \( k=-9 \).

Step2: Analyze horizontal shift

Since \( h = 2>0 \), horizontal shift is 2 units to the right.

Step3: Analyze vertical shift

Since \( k=-9<0 \), vertical shift is 9 units downward.

Answer:

a) 2; right; 9; downward