I'm not sure, but I know that it is longer than 5
The quadratic formula is x equals negative b plus or minus the square root of b squared minus four times a times c, all over 2a.
Looking at the equation, we can find the values for a, b, and c
a=7
b= -10
c= -2
So then putting that back into standard form, which is ax^2+bx+c, we know Haley's function in standard form is 7x^2-10x-2
8080=6 because there are 6 "0s" or circle shaped objects that make up the number. For example, 8=2 (there are two circles.)
<u>Using the same logic,</u>
1357=0 because there are no circles.
2022=1; there is 1 circle.
1999=3; three circles.
6666=4; there are four circles.
When values of a quadratic function are listed in a table with x-values having a constant difference, the y-vlaues will have a constant (non-zero) second-difference.
Here, we can list first and second differences for the values in the given tables to identify the quadratic function.
Table 1.
- 1st differences: 3, 3, 3, 3
- 2nd differences: 0, 0, 0, 0 . . . . this is a linear function
Table 2.
- 1st differences: -6, -2, 2, 6
- 2nd differences: 4, 4, 4 . . . . this is a quadratic function
Table 3.
- 1st differences: 5, -8, -3, -3
- 2nd differences: -13, 5, 0 . . . . can be described by a 4th degree polynomial
Table 4.
- 1st differences: 3, 0, -3, -3
- 2nd differences: -3, -3, 0 . . . . can be described by a 4th degree polynomial
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The appropriate choice is Table 2.