Answer:
Rui will reach his lowest altitude after diving for 10 seconds
Step-by-step explanation:
In the quadratic equation y = ax² + bx + c, the coordinates of the lowest or the highest point is (h, k), where
- h = [tex]\frac{-b}{2a}[/tex] and k = y at x = h
In the given question
∵ d(x) = [tex]\frac{1}{2}[/tex] x² - 10 x
∵ d represents his altitude in meters after x seconds
→ Compare it with the form above to find a and b
∴ a = [tex]\frac{1}{2}[/tex] and b = -10
∵ h = [tex]\frac{-b}{2a}[/tex]
→ Substitute the values of a and b in the rule to find h
∴ h = [tex]\frac{--10}{2.\frac{1}{2}}[/tex] = 10
∴ h = 10
∵ h is the x-coordinate of the lowest point
∴ The time of the lowest altitude is 10 seconds
∴ Rui will reach his lowest altitude after diving for 10 seconds
