Question

1. how does adding a constant to $y = ax^2$ affect the parabola?

a. stretches it horizontally
b. opens it downward
c. narrows it
d. shifts it upward

Explanation:

Adding a constant \(k\) to \(y = ax^2\) gives \(y = ax^2 + k\). When \(k>0\), the parabola shifts upward; when \(k<0\), it shifts downward. Among the options, shifting upward is a valid vertical shift result of adding a positive constant, while the other options describe changes from modifying \(a\) (stretching/narrowing) or flipping the parabola (opening downward, which comes from negative \(a\)).

Answer:

d. Shifts it upward