The equation of the parabola is gotten as;
y = -4x² + 24x - 32
We are given the coordinates of a parabola to be;
(3, 4) ; (4,0) ; (2,0)
The general form of equation of a parabola is given by;
y = ax² + bx + c
Let's plug in the x and y coordinates as given to us from the question.
- For coordinate (3, 4), the equation is;
(3²)a + 3b + c = 4
9a + 3b + c = 4 ----(eq 1)
- For coordinate (4, 0), the equation is;
(4²)a + 4b + c = 0
16a + 4b + c = 0 ----(eq 2)
- For coordinate (2, 0), the equation is;
(2²)a + 2b + c = 0
4a + 2b + c = 0 ----(eq 3)
- Solving the 3 equations using an online simultaneous equation solver tool, we have; a = -4; b = 24; c = -32
- Plugging these values of a, b and c into the general equation of parabola gives us;
y = -4x² + 24x - 32
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