y = x² + 3x + 10
the equation of a parabola in standard form is → y = ax² + bx + c ( a ≠ 0 )
Substitute each of the pairs of coordinate points into the equation and solve for a, b and c
(- 2, 8) → 8 = 4a + 2b + c → (1)
(1, 14) → 14 = a + b + c → (2)
note that (0 , 10) is the y-intercept ⇒ c = 10
substitute c = 10 into (1) and (2)
8 = 4a - 2b + 10 → 4a - 2b = - 2 → (3)
14 = a + b + 10 → a + b = 4 → (4)
multiply (4 ) by 2
2a + 2b = 8 → (5)
add (3) and (5) term by term ⇒ 6a = 6 ⇒ a = 1
substitute a = 1 into (4)
1 + b = 4 ⇒ b = 3
thus a = 1, b= 3 and c = 10
equation of parabola is y = x² + 3x + 10
