Answer:
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
Step-by-step explanation:
x-coordinate of the vertex of a parabola is ( [tex]- \frac{b}{2a}[/tex] )
y = f(x) = ax² + bx + c
(x, y) ∈ f(x)
~~~~~~~~~
{ (0, - 2), (3, - 5) } ⊂ { (x, y): y = ax² + bx + c }
a(0)² + b(0) + c = - 2 ⇒ c = - 2
a(3)² + b(3) + ( - 2) = - 5
9a + 3b - 2 = - 5 ⇒ 3a + b = - 1
[tex]- \frac{b}{2a}[/tex] = 3 ⇒ b = - 6a
[tex]\left \{ {{3a+b=-1} \atop {b=-6a}} \right.[/tex]
3a + ( - 6a) = - 1
a = [tex]\frac{1}{3}[/tex]
b = - 2
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
