The quadratic equation represented in the table is:
y = 100.875x² - 3.75x
How to find the quadratic equation?
The general quadratic is written as.
y = ax² + bx + c
The first pair in the table is (0, 0), then:
0 = a*0² + b*0 + c
0 = c
y = ax² + bx
Using the next two pairs we can set up the equations:
396 = 4a + 2b
1599 = 16a + 4b
From the first one we can write:
2b = 396- 4a
Replace that in the other equation:
1599 = 16a + 2*(2b)
1599 = 16a + 2*(396- 4a)
1599 = 16a + 792 - 8a
Solving for a:
a = (1599 - 792)/8 = 100.875
And the value of b is:
b = (396 - 4*100.875)/2
b = -3.75
Then the quadratic is:
y = 100.875x² - 3.75x