Question

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.

Answer 1

Answer:

The factor version is

$(x + 8)(x - 3)$

The x intercepts are

(-8,0)

(3,0).

Step-by-step explanation:

$- {x}^{2} + 5x + 24$

We can factor this into

$(x + y)(x + p)$

Where y and p are numbers that

• Multiply to -24
• Add to 5.

Those two numbers are 8,-3. So our factored version is

$(x + 8)(x - 3)$

Set each factor to zero.

$x + 8 = 0$

$x = - 8$

$x - 3 = 0$

$x = 3$