Question

1. if a parabola has its vertex at ( x = 5 ) and opens upward, which of the following correctly describes its increasing interval? a. ( (5,infty) ) b. ( (0,5) ) c. ( (-infty,5) ) d. ( (-infty,0) )

Explanation:

Step1: Recall the properties of a parabola

For a parabola \(y = a(x - h)^2 + k\) (vertex form), if \(a>0\) (opens upward), the vertex is \((h,k)\). The function is decreasing on the interval \((-\infty,h)\) and increasing on the interval \((h,\infty)\).

Step2: Identify \(h\) value

Given the vertex \(x = 5\), so \(h = 5\). Since the parabola opens upward (\(a>0\)), the increasing interval is \((5,\infty)\).

Answer:

A. \((5,\infty)\)