Answer:
[tex]f(x)=4x^2[/tex]
Step-by-step explanation:
Quadratic Model
The quadratic function can be expressed in the form:
[tex]f(x)=ax^2+bx+c[/tex]
Where a,b, and c are constants to be determined using the points through which the function passes.
We have the points (-2,16) (0,0) (1,4). To find the values of a,b,c we just substitute the values of x and y and solve the system of equations.
Point (0,0):
[tex]f(0)=a*0^2+b*0+c=0[/tex]
It follows that
c=0
Point (-2,16):
[tex]f(0)=a*(-2)^2+b*(-2)+c=16[/tex]
Operating:
[tex]a*(4)+b*(-2)+c=16[/tex]
Since c=0:
[tex]4a-2b=16[/tex]
Divide by 2:
[tex]2a-b=8\qquad\qquad [1][/tex]
Point (1,4):
[tex]f(1)=a*(1)^2+b*(1)+c=4[/tex]
[tex]a*(1)+b*(1)+c=4[/tex]
Since c=0:
[tex]a+b=4\qquad\qquad [2][/tex]
Adding [1] + [2]:
2a+a=12
3a=12
a=12/3=4
a=4
From [2]
b=4-a
b=4-4=0
b=0
The model is:
[tex]\boxed{f(x)=4x^2}[/tex]
