The quadratic function is [tex]y=1x^{2} + (-8)x + 4[/tex]
Step-by-step explanation:
The quadratic function given is [tex]ax^{2} + bx + c=y[/tex]
and same quadratic function is passes through (-3,37), (2,-8), (-1,13)
Replacing points one by one
we get,
For (-3,37) :
[tex]a(-3)^{2} + b(-3) + c=37[/tex]
[tex]9a + -3b + c=37[/tex] = equation 1
For (2,-8) :
[tex]a(2)^{2} + b(2) + c=(-8)[/tex]
[tex]4a + 2b + c=(-8)[/tex] = equation 2
For (-1,13)
[tex]a(-1)^{2} + b(-1) + c=(13)[/tex]
[tex]a + -1b + c=13[/tex] = equation 3
Solving the linear equation to get values of a,b,c
Subtract equation 2 with equation 3
we get,[tex](4a + 2b + c)-(a + -1b + c)=(-8)-13[/tex]
[tex](3a + 3b )=(-21)[/tex]
[tex](a + b )=(-7)[/tex] = equation 4
Now, Subtract equation 1 with equation 2
we get,[tex](9a + -3b + c)-(4a + 2b + c)=(37)-(-8)[/tex]
[tex](5a - 5b )=(45)[/tex]
[tex](a - b )=(9)[/tex] = equation 5
Now, Add equation 4 with equation 5
we get,[tex](a + b)+(a - b)=(-7)+(9)[/tex]
[tex](2a - 0b )=(2)[/tex]
[tex](a)=1[/tex]
Replacing value of a in equation 5
[tex](a - b )=(9)[/tex]
[tex](1 - b )=(9)[/tex]
[tex](b)=(-8)[/tex]
Replacing value of a and b in equation 1
[tex]9a + -3b + c=37[/tex]
[tex]9(1) + -3(-8) + c=37[/tex]
[tex]9 + 24 + c=37[/tex]
[tex] c=4[/tex]
Thus,
The quadratic function [tex]y=1x^{2} + (-8)x + 4[/tex]
