The equation of the parabola is y = 5x² - 11x - 31
Parabola
The equation of a parabola is a quadratic equation in the form:
y = ax² + bx + c
Where a, b and c are constants.
At point (2, - 33):
- -33 = a(2)² + b(2) + c
- 4a + 2b + c = -33 (1)
At point (4, 5):
- 5 = a(4)² + b(4) + c
- 16a + 4b + c = 5 (2)
At point (5, 39):
- 39 = a(5)² + b(5) + c
- 25a + 5b + c = 39 (3)
Solving equation 1, 2 and 3 simultaneously gives:
a = 5, b = -11, c = -31.
The equation of the parabola is y = 5x² - 11x - 31
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