Answer:[tex]x^2-5x=-12(y+2)[/tex]
Step-by-step explanation:
Given
Parabola has x-intercept has [tex](3,0)[/tex] and [tex](8,0)[/tex]
and Y-intercept as [tex](0,-2)[/tex]
Now the general equation of parabola is
[tex]y=ax^2+bx+c\quad \ldots(i)[/tex]
Substitute [tex](0,-2)[/tex] in [tex](i)[/tex] we get
[tex]-2=c[/tex]
Now substitute [tex](3,0)[/tex] in equation [tex](i)[/tex]
[tex]0=a(3)^2+3b-2\quad \ldots(ii)[/tex]
Now substitute [tex](8,0)[/tex] in equation [tex](i)[/tex]
[tex]0=a(8)^2+8b-2\quad \ldots(iii)[/tex]
Solving [tex](ii)[/tex] and [tex](iii)[/tex] we get
[tex]a=\frac{-1}{12}\ \text{and}\ b=\frac{5}{12}[/tex]
therefore
[tex]y=\frac{-x^2}{12}+\frac{5x}{12}-2[/tex]
[tex]12y=-x^2+5x-24[/tex]
