The equation of a parabola is expressed as
y = ax^2 + bx + c
From the information, the given points are
x-intercept : (0.9,0)
y- intercept : (0, -1.4)
3rd point: (2,0.6)
The first step is to substitute x = 0.9 and y = 0 into the equation. We have
0 = a(0.9)^2 + b(0.9) + c
0 = 0.81a + 0.9b + c equation 1
The next step is to substitute x = 0 and y = - 1.4 into the equation. We have
- 1.4 = a(0)^2 + b(0) + c
- 1.4 = c equation 2
The next step is to substitute x = 2 and y = 0.6 into the equation. We have
0.6 = a(2)^2 + b(2) + c
0.6 = 4a + 2b + c equation 3
We would substitute c = - 1.4 into equations 1 and 3.
Substituting c = equation 1, it becomes
0 = 0.81a + 0.9b - 1.4
0.81a + 0.9b = 1.4 equation 4
Substituting c = equation 3, it becomes
0.6 = 4a + 2b - 1.4
4a + 2b = 0.6 + 1.4
4a + 2b = 2
Dividing through by 2, it becomes
2a + b = 1
b = 1 - 2a
Substituting b = 1 - 2a into equation 4, it becomes
0.81a + 0.9(1 - 2a) = 1.4
0.81a + 0.9 - 1.8a = 1.4
0.81a - 1.81a = 1.4 - 0.9
- a = 0.5
Dividing both sides by - 1,
- a/- 1 = 0.5/- 1
a = - 0.5
Substituting a = - 0.5 into b = 1 - 2a, we have
b = 1 - 2(- 0.5)
b = 1 + 1
b = 2
Finally, we would substitute a = - 0.5, b = 2 and c = - 1.4 into the equation of the parabola, the equation of the given parabola is
y = - 0.5x^2 + 2x - 1.4