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The parabola passes through the points A(0, 8), B(3, 0) and C(-3,0).
The equation of the parabola is of the form y = ax^2 + bx + c.
To determine the value of c, the equation y = ax^2 + bx + c should be solved for the coordinates (0,8).
8 = a*0 + b*0 + c
c = 8
To determine a and b, y = ax^2 + bx + c should be solved for the coordinates (3,0) and (-3,0)
0 = a*(-3)^2 - 3b + c
0 = a*(3)^2 + 3b + c
As c = 8
9a - 3b + 8 = 0 and 9a + 3b + 8 = 0
Adding the two equations, 18a + 16 = 0
a = -16/18
b = 0
The graph of the parabola y = (-16/18)x^2 + 8 is:
The parabola y = (-16/18)x^2 + 8 passes through all the points A, B and C as described in the question.
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