Answer:
[tex]y=3x^2-5x-2[/tex]
Step-by-step explanation:
Let the quadratic function be
[tex]y=ax^2+bx+c[/tex]
The given points must satisfy this function;
Substitute [tex](-2,20)[/tex].
[tex]20=4a-2b+c..(1)[/tex]
Substitute (0,-2)
[tex]c=-2...(2)[/tex]
Substitute (1,-4);
[tex]-4=a+b+c...(3)[/tex]
Put equation (2) into equation (1)
[tex]20=4a-2b+-2[/tex]
[tex]4a-2b=22[/tex]
[tex]2a-b=11...(4)[/tex]
Put equation (2) into equation (3)
[tex]-4=a+b-2...(3)[/tex]
[tex]a+b=-2...(5)[/tex]
Add equation (4) and (5)
[tex]3a=9[/tex]
Divide both sides by 3
[tex]a=3[/tex]
Put a=3 in equation 5.
[tex]3+b=-2[/tex]
[tex]b=-2-3[/tex]
[tex]b=-5[/tex]
The quadratic function is;
[tex]y=3x^2-5x-2[/tex]
