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.
