Question

Which quadratic rule represents the data in the table?

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

Please help me i literally been doing this problem for 30 minutes, i think its B but my math doesn't go with it..

Edit: I'm not sure why it says high school, I'm in 8th grade

Answer 1

To find the quadratic rule that represents the data in the table, we need to look for a quadratic equation in the form y = ax^2 + bx + c that fits the given values of x and y.

Using the given data, we can set up a system of three equations with three unknowns (a, b, and c) to solve for the coefficients:

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 each equation, we get:

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

Substituting c = 5 into the first equation, we get:

a - b = -1

Subtracting this equation from the second equation, we get:

2b = 5

b = 5/2

Substituting b = 5/2 and c = 5 into the first equation, we get:

a = -3/2

Therefore, the quadratic rule that represents the data in the table is:

y = -3/2x^2 + 5/2x + 5

So the closest option is A. y = –2x^2 + 5, but it is not the correct quadratic rule that represents the data in the table.