Given three points of a quadratic function, find the equation that defines the function: (0,-,-3)(1,5)

a: f(x)=4x^2+6x+5
b: f(x)=6x^2+4x+5
d: f(x)=6x^2+4x-5

D

Step-by-step explanation:

The standard form of a quadratic function is

y = ax² + bx + c : a ≠ 0

Substitute the 3 points into the equation to solve for a, b and c

(0, - 5 ) : 0 + 0 + c = - 5 ⇒ c = - 5

(-1, - 3 ) : a - b - 5 = - 3 ⇒ a - b = - 3 + 5 = - 2 → (1)

(1, 5 ) : a + b - 5 = 5 ⇒ a + b = 5 + 5 = 10 → (2)

Add (1) and (2) term by term to eliminate b

2a = 12 ⇒ a = 6

substitute a = 6 into (2)

6 + b = 10 ⇒ b = 10 - 6 = 4

a = 6, b = 4 and c = - 5, Hence equation is

y = 6x² + 4x - 5 → D