Determine whether the given table of values represents a quadratic function x= -1 / 0 /1 / 2 / 3
y= 4 / 3 / 4 / 7 / 12
starting at x=0, the 2nd differences are constant (2) so yes, it is a quadratic
y = x^2+3
The difference between x-values is constant so use differences of y- values to determine the model.
If the second difference is the same value, the model will be quadratic.
First difference of y-values:
3 - 4 = - 1
4 - 3 = 1
7 - 4 = 3
12 - 7 = 5
Second difference of y-values:
1 - ( - 1 ) = 1 + 1 = 2
3 - 1 = 2
5 - 3 = 2
The second difference is the same value, so the given table of values represents a quadratic function.
By the way this quadratic function is:
y = x^2 + 3
To determine whether the given table of values represents a quadratic function, one way is to check if the second differences between the y-values are constant. Let's calculate the second differences:
x: -1 0 1 2 3
y: 4 3 4 7 12
First differences:
∆y₁ = 3 - 4 = -1
∆y₂ = 4 - 3 = 1
∆y₃ = 7 - 4 = 3
∆y₄ = 12 - 7 = 5
Second differences:
∆²y₁ = 1 - (-1) = 2
∆²y₂ = 3 - 1 = 2
∆²y₃ = 5 - 3 = 2
Since the second differences (∆²y) are constant (equal to 2 in this case), this indicates that the given table of values represents a quadratic function.
Therefore, the given table of values represents a quadratic function.
To determine whether the given table of values represents a quadratic function, we need to observe the pattern and see if it fits a quadratic relationship.
Step 1: Identify the x-values and y-values in the table:
x = -1, 0, 1, 2, 3
y = 4, 3, 4, 7, 12
Step 2: Calculate the differences between consecutive y-values:
Δy1 = 3 - 4 = -1
Δy2 = 4 - 3 = 1
Δy3 = 7 - 4 = 3
Δy4 = 12 - 7 = 5
Step 3: Calculate the differences between consecutive differences:
Δ²y1 = 1 - (-1) = 2
Δ²y2 = 3 - 1 = 2
Δ²y3 = 5 - 3 = 2
If the differences between consecutive differences are equal, then the table represents a quadratic function.
In this case, since the differences between consecutive differences are all equal to 2, the given table of values represents a quadratic function.