Jen and her friends are designing a robot for a STEM competition. The goal of the competition is to have a robot complete an obstacle course in the least amount of time.
Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course. The director of the competition laid out components of the obstacle course on a coordinate plane. Instead of giving the width and maximum height of the arch, the director created an expression based on the location of the arch on the coordinate plane and gave each team this expression to represent the height of the arch, in inches, at any value of x along the arch:
-x2 + 5x + 24.

Factor the expression, and use the factors to find the x-intercepts of the quadratic relationship it represents.
Type the correct answer in each box, starting with the intercept with the lower value.
The x-intercepts occur where x = and x = .