Answer:
The quadratic equation is y = [tex]x^{2} - 4x +3[/tex]
Step-by-step explanation:
Let the quadratic equation be y = f(x) = [tex]ax^{2} +bx+c[/tex]
The graph of this quadratic equation should pass through all the given points.
The given points are (-1,8),(2,-1) and (0,3).
y = [tex]ax^{2} +bx+c[/tex]
We have to substitute the 3 points in the general equation and solve to find the values of a,b and c.
Substitute (-1,8) ,
8 = [tex]a(-1)^{2} + b(-1) + c[/tex]
8=a - b + c -------------------------(1)
Substitute (2,-1) ,
-1 = [tex]a(2)^{2} + b(2) +c[/tex]
-1 = 4a + 2b + c --------------------------(2)
Substitute (0,3) ,
3 = [tex]a(0)^{2} + b(0) +c[/tex]
3 = c
c = 3 --------------------------(3)
Substitute (3) in (1) and (2) ,
8 = a - b + c
8 = a - b + 3
a - b = 5
a = b + 5 --------------------------(4)
4a + 2b + c = -1
4a + 2b + 3 = -1
4a + 2b = -4
2a + b = -2 --------------------------(5)
Substitute (4) in (5) ,
2a + b = -2
2\times (b + 5) + b = -2
2b +10 +b = -2
b = -4
Substituting value of b in (4) ,
a = 1
Hence the quadratic equation is y = [tex]x^{2} - 4x +3[/tex]
