Answer:
f(x) = -3x² + 7x + 1
Step-by-step explanation:
When parabola f(x) = ax² + bx + c passes through point (x₁, y₁) that means if x=x₁ then f(x)=f(x₁)=y₁
(0, 1) ⇒ 1=a·0²+b·0+c ⇒ c=1
f(x) = ax² + bx + 1
(1, 5) ⇒ 5 = a·1² + b·1 + 1
5 = a + b + 1
-b = a - 4
b = - a + 4
(2, 3) ⇒ 3 = a·2² + b·2 + 1
3 = 4a + 2b + 1
-2b = 4a - 2
b = - 2a + 1
- a + 4 = - 2a + 1
a = - 3
b = -(-3) + 4 = 7
So the equation:
f(x) = -3x² + 7x + 1
