Please Help!
Which quadratic rule represents the data in the table?
x -1, 0, 1, 2, 3
y 6, 5, 6, 9, 14
a. y= -2x^2 + 5
b. y= -x^2 + 5**
c. y= x^2 - 5
d. y= x^2 + 5
nope. when x=1, -1^2+5 = -1+5 = 4
To determine which quadratic rule represents the data in the table, we can first look for a pattern in the values of x and y. Let's analyze the table:
x: -1, 0, 1, 2, 3
y: 6, 5, 6, 9, 14
From the given values, we can see that when x increases by 1, the value of y either increases or decreases.
To find the quadratic rule, we need to check whether the data follows a pattern that matches the general form of a quadratic equation: y = ax^2 + bx + c, where a, b, and c are constants.
We can start by substituting the x and y values from the table into the equation options and see which equation matches the data.
a. y = -2x^2 + 5
Substituting the x values:
For x = -1, y = -2(-1)^2 + 5 = -2 + 5 = 3 (not a match)
For x = 0, y = -2(0)^2 + 5 = 0 + 5 = 5 (a match)
For x = 1, y = -2(1)^2 + 5 = -2 + 5 = 3 (not a match)
For x = 2, y = -2(2)^2 + 5 = -8 + 5 = -3 (not a match)
For x = 3, y = -2(3)^2 + 5 = -18 + 5 = -13 (not a match)
b. y = -x^2 + 5
Substituting the x values:
For x = -1, y = -(-1)^2 + 5 = -1 + 5 = 4 (not a match)
For x = 0, y = -(0)^2 + 5 = 0 + 5 = 5 (a match)
For x = 1, y = -(1)^2 + 5 = -1 + 5 = 4 (not a match)
For x = 2, y = -(2)^2 + 5 = -4 + 5 = 1 (not a match)
For x = 3, y = -(3)^2 + 5 = -9 + 5 = -4 (not a match)
c. y = x^2 - 5
Substituting the x values:
For x = -1, y = (-1)^2 - 5 = 1 - 5 = -4 (not a match)
For x = 0, y = (0)^2 - 5 = 0 - 5 = -5 (not a match)
For x = 1, y = (1)^2 - 5 = 1 - 5 = -4 (not a match)
For x = 2, y = (2)^2 - 5 = 4 - 5 = -1 (not a match)
For x = 3, y = (3)^2 - 5 = 9 - 5 = 4 (not a match)
d. y = x^2 + 5
Substituting the x values:
For x = -1, y = (-1)^2 + 5 = 1 + 5 = 6 (a match)
For x = 0, y = (0)^2 + 5 = 0 + 5 = 5 (a match)
For x = 1, y = (1)^2 + 5 = 1 + 5 = 6 (a match)
For x = 2, y = (2)^2 + 5 = 4 + 5 = 9 (a match)
For x = 3, y = (3)^2 + 5 = 9 + 5 = 14 (a match)
By comparing the values of y from the given data with the equations, we can see that option b. y = -x^2 + 5 matches the given data from the table.