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:

When a constant \(k\) is added to \(y = ax^2\) to get \(y = ax^2 + k\), this represents a vertical translation of the parabola. If \(k>0\), the parabola shifts upward; if \(k<0\), it shifts downward. The other options describe transformations from multiplying the function (stretching/narrowing) or changing the sign of \(a\) (opening downward), not adding a constant.

Answer:

d. Shifts it upward