Question

Determine whether a quadratic model exists for each set of values. If so, write the model.

Answer 1

Answer:

$f(x)=4x^2$

Step-by-step explanation:

Quadratic Model

The quadratic function can be expressed in the form:

$f(x)=ax^2+bx+c$

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):

$f(0)=a*0^2+b*0+c=0$

It follows that

c=0

Point (-2,16):

$f(0)=a*(-2)^2+b*(-2)+c=16$

Operating:

$a*(4)+b*(-2)+c=16$

Since c=0:

$4a-2b=16$

Divide by 2:

$2a-b=8\qquad\qquad [1]$

Point (1,4):

$f(1)=a*(1)^2+b*(1)+c=4$

$a*(1)+b*(1)+c=4$

Since c=0:

$a+b=4\qquad\qquad [2]$

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:

$\boxed{f(x)=4x^2}$