which quadratic rule represents the data in the table?

Question

X |-1 | 0 | 1 | 2 | 3 |
Y | 4 | 5 | 4 | 1 | -4|

A: y= -2x^2+5
B: y= -x^2+5
C: y= x^2-5
D: y= x^2+5

Answer 1

The correct answer is B: y= -x^2+5.

To determine the quadratic rule, we need to fit a quadratic equation of the form y = ax^2 + bx + c to the given data points.

Substituting the x and y values from the table into the equation, we get the following system of equations:

4 = a(-1)^2 + b(-1) + c
5 = a(0)^2 + b(0) + c
4 = a(1)^2 + b(1) + c
1 = a(2)^2 + b(2) + c
-4 = a(3)^2 + b(3) + c

Simplifying these equations gives:

a - b + c = 4
c = 5
a + b + c = 4
4a + 2b + c = 1
9a + 3b + c = -4

Solving this system of equations (by substitution or elimination) gives a = -1, b = 0, and c = 5.

Therefore, the quadratic rule that represents the data in the table is y = -x^2 + 5.