Question

find the effect of the change to the graph of the parent function of $y = x^2 - 3$.

\bigcirc shifted 3 units up

\bigcirc shifted 3 units down

\bigcirc shifted 3 units left

\bigcirc shifted 3 units right

Explanation:

Step1: Recall Parent Function

The parent function of \( y = x^2 - 3 \) is \( y = x^2 \) (the basic quadratic function).

Step2: Analyze Vertical Shift Rule

For a function \( y = f(x) + k \), if \( k>0 \), the graph shifts up \( k \) units; if \( k<0 \), it shifts down \( |k| \) units. Here, \( y = x^2 - 3 \) can be written as \( y = x^2 + (-3) \), so \( k = -3 \). This means the graph of \( y = x^2 \) is shifted down 3 units.

Answer:

B. Shifted 3 units down (assuming the second option is labeled as B; if original options have labels like A, B, etc., adjust accordingly. Based on the options, the correct one is "Shifted 3 units down".)