Let the first number = x
The second number would be x +1
3rd number = x +2
4th number = x +3
5th number = x+4
6th number = x+5
7th number = x +6
8th number = x +7
9th number = x+8
The sum is 279
Combine like terms in the 9 numbers to get: 9x + 36 = 279
Solve for x:
9x + 36 = 279
Subtract 36 from both sides:
9x = 243
Divide both sides by 9:
x =27
The first number is 27
The last number would be 27 + 8 = 35
The sum of the first and last would be 27 + 35 = 63
The vertex is at (2, 5).
To find the vertex, we first find the axis of symmetry; this is given by
x = -b/2a
For our equation, b = -16 and a = 4:
x = -(-16)/2(4) = 16/8 = 2
We substitute this back into our equation:
y = 4(2)² - 16(2) + 21 = 4(4) - 32 + 21 = 5
Therefore the vertex is at (2, 5).
