Answer:
y = 3x² – 9b + 3 and the parabola opens upwards since a = 3 > 0.
Step-by-step explanation:
The general equation of a parabola is:
y = ax² + bx + c
So we have to solve for a, b and c to get our equation with the 3 given points.
When x = 0 and y = 3 we have
3 = a(0)² + b(0) + c, this means c = 3
When x = 4 and y = 15
15 = a(4)² + b(4) + 3 we have
16a + 4b = 12 which is
4a + b = 3
When x = 5 and y = 33 we have
33 = a(5)² + b(5) + 3 we have
25a + 5b = 30 which gives
5a + b = 6.
We have two equations
4a + b = 3
5a + b = 6
Eliminating b we have
a = 3, substituting a = 3 in the first equation we have
4(3) + b = 3
12 + b = 3
b = –9
Our equation therefore is:
y = 3x² – 9b + 3 and the parabola opens upwards since a = 3 > 0.
