Given
The coordinates are given
y- intercept : (0, -1.4)
x-intercept : (0.905,0)
3rd point: (2,0.6)
Explanation
To find the equation of parabola , use the general equation of parabola
[tex]y=ax^2+bx+c[/tex]
Substitute the values in the equation.
1. (0, -1.4)
[tex]\begin{gathered} -1.4=a(0)^2+b(0)+c \\ c=-1.4 \end{gathered}[/tex]
2. (0.905,0)
[tex]\begin{gathered} 0=a(0.905)^2+b(0.905)-1.4 \\ 0.819025a+0.905b-1.4=0\ldots\ldots\ldots\text{.}.1 \end{gathered}[/tex]
3.(2,0.6)
[tex]\begin{gathered} 0.6=4a+2b-1.4 \\ 4a+2b=2 \\ 2a+b=1 \\ b=1-2a \end{gathered}[/tex]
Substitute the value of b=1-2a in the equation 1.
[tex]\begin{gathered} 0.819025a+0.905(1-2a)-1.4=0 \\ 0.819025a+0.905-1.81a-1.4=0 \\ -0.990975a=0.495 \\ a=-0.4995 \end{gathered}[/tex]
Find the value of b ,
[tex]\begin{gathered} b=1-2\times(-0.4995) \\ b=1.999 \end{gathered}[/tex]
Therefore , the value of a is -0.4995, b is 1.999 and c is -1.4.
Answer
The equation of parabola is obtained as
[tex]y=-0.4995x^2+1.999x-1.4[/tex]
