Question

Write an eqution to the table. y x 3 1 1.5 2 1 3

Answer 1

Answer:

$f(x)=0.5x^2-3x+5.5$

Step-by-step explanation:

We can see by some observation that this is not linear because the slopes aren't constant.

So, let's see if it's quadratic. Suppose that it is and the function we want to find is: $f(x)=ax^2+bx+c$

Plug in some of the given values into the equation:

3 = a + b + c               ------------ eq 1

1 = 9a + 3b + c           ------------ eq 2

1.5 = 4a + 2b + c        ------------ eq 3

Let's multiply eq 3 by 2 and then subtract it from equation 2:

   1 =  9a + 3b + c

-  3 = 8a + 4b + 2c

----------------------------

  -2 = a - b - c

Now, add this equation to eq 1:

   -2 = a - b - c

+   3 = a + b + c

-----------------------

    1 = 2a

    a = 1/2 = 0.5

Now, plug this value of a back into both eq 3 and eq 1:

Eq 3: 1.5 = 4 * 0.5 + 2b + c  ⇒  1.5 = 2 + 2b + c  ⇒  -0.5 = 2b + c     ----- eq 5

Eq 1: 3 = 0.5 + b + c  ⇒  b + c = 2.5   ------ eq 4

So, we have a system of linear equations. Subtract eq 4 from eq 5:

    2b + c = -0.5

-      b + c = 2.5

-------------------------

      b = -3

Substitute this value of b into b + c = 2.5 and solve for c:

-3 + c = 2.5

c = 5.5

So, a = 0.5, b = -3, and c = 5.5. Now, our equation is:

$f(x)=0.5x^2-3x+5.5$

Hope this helps!

Answer 2

Answer:

y = 3/x

Step-by-step explanation:

y = 3/x

xy = 3

3×1 = 3

1.5×2 = 3

1×3 = 3