Question

HELP!!! URGENT!!! I WILL GIVE BRAINLEIST THING ​

Answer 1

Answer:

Horizontal distance = 0 m and 6 m

Step-by-step explanation:

Height of a rider in a roller coaster has been defined by the equation,

y = $\frac{1}{3}x^{2}-2x+8$

Here x = rider's horizontal distance from the start of the ride

i). $y=\frac{1}{3}x^{2}-2x+8$

      $=\frac{1}{3}(x^{2}-6x+24)$

      $=\frac{1}{3}[x^{2}-2(3x)+9-9+24]$

      $=\frac{1}{3}[(x^{2}-2(3x)+9)+15]$

      $=\frac{1}{3}[(x-3)^2+15]$

      $=\frac{1}{3}(x-3)^2+5$

ii). Since, the parabolic graph for the given equation opens upwards,

    Vertex of the parabola will be the lowest point of the rider on the roller coaster.

    From the equation,

    Vertex → (3, 5)

    Therefore, minimum height of the rider will be the y-coordinate of the vertex.

    Minimum height of the rider = 5 m

iii). If h = 8 m,

    $8=\frac{1}{3}(x-3)^2+5$

    $3=\frac{1}{3}(x-3)^2$

    (x - 3)² = 9

    x = 3 ± 3

    x = 0, 6 m

    Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m