Answer:
f(x) = x² - 6x + 3
Step-by-step explanation:
Parabola f(x) = ax² + bx + c passing through point (x₁, y₁) means if x=x₁ then f(x)=f(x₁)=y₁
(0, 3) ⇒ 3=a·0²+b·0+c ⇒ c=3
f(x) = ax² + bx + 3
(4, -5) ⇒ -5 = a·4² + b·4 + 3
-5 = 16a + 4b + 3
-4b = 16a + 8
b = - 4a - 2
(-1, 10) ⇒ 10 = a·(-1)² + b·(-1) + 3
10 = a - b + 3
b = a - 7
a - 7 = - 4a - 2
5a = 5
a = 1
b = 1 - 7 = - 6
So the equation:
f(x) = x² - 6x + 3
