Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
The equation of the curve is;
Using the points;
(4, 4), (2, 0), (12, 0)
And, y =ax²+bx+c
Therefore;
4=16a+4b+c
0=4a+2b+c
0=144a+12b+c
Solving the three equations via matrix determinant approach.
It implies;
a = -¼, b = ½(7) and c = -6
Substituting a, b and c values in the standard quadratic equation.
The equation of the curve is;
y = -¼(x²) + ½(7x) - 6
The maximum turning point of the curve is;
At y = 6¼
And the x-axis at the maximum turning point is;
x = 7
It implies;
Area grey, exactly in its decimal square units form is;
Area under the curve at the points (7, 0) and (12, 0) - Area triangle with height 2.25 units and base 3.85714285718 units + Area triangle with side 4 units and √(769)/8 units, and angle atan(12/25)°
= (125/6) - ½(2.25*3.85714285718) + ½(4*(√(769)/8))sin(atan(12/25)))
= (125/6) - 4.33928571433 + 3
= 19.494047619 square units.
