Question

I know that this is a lot but I really need help!! Hopefully, the reward will help!

Answer 1

Step-by-step explanation:

y = 2/27 x² − 4/3 x

a) The leading coefficient (the coefficient of the x² term) is positive, so that means the parabola points up.  So the vertex is at the bottom of the parabola, making it a minimum.

b) For a parabola y = ax² + bx + c, the x coordinate of the vertex can be found at x = -b / (2a).  Here, a = 2/27 and b = -4/3.

x = -(-4/3) / (2 × 2/27)

x = (4/3) / (4/27)

x = (4/3) × (27/4)

x = 9

c) To find the y coordinate of the vertex, we simply evaluate the function at x=9:

y = 2/27 x² − 4/3 x

y = 2/27 (9)² − 4/3 (9)

y = 6 − 12

y = -6

d) The ordered pair is (9, -6).  This means that at the lowest point of the dish, the dish is 6 inches deep.  Also, since the dish is symmetrical, and the lowest point is 9 inches from the end, then the total width is double that, or 18 inches.