exam Maths Puzzle Numerical Ability

How do I proceed with this problem?
Find a, b, and c such that the graph of y= ax^2 + (b times the square root of x) + c goes through the points (0,3), (1,-1/2), and (4,3). Any help would be much appreciated.

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exam Other Question

The width of a rectangular box is 4 times its height, and its length is 3 ft more than its height. The volume of the box is 49 ft cube. Find the height of the box.

volume = lwh
49 = (4x)(3+x)(x)
49 = 4x3 +12x2
did i do this right?
rounded 2 decimal places the approximate x intercept of the equation x^3+14.2x^2-4.8x-12.4=0
in standard window
i got 53.44??????????????