Write the equation of the quadratic function that passes through the points (3,2) , (2,5) and (1,4) in vertex form

Question

Write the equation of the quadratic function that passes through the points (3,2) , (2,5) and (1,4) in vertex form

Answer 1

y = ax² + bx + c       
Substitute each point into this equation in order to find a, b, and c.

(3,2): 2 = 9a + 3b + c     (Eq.#1)

(2,5): 5 = 4a + 2b + c     (Eq.#2)

(1,4): 4 = a + b + c         (Eq#3)²

Subtract Eq.#3 from Eq.#2

   5 = 4a + 2b + c

-(4 = a + b + c)

   1 = 3a + b    (Eq.#4)

Now subtract Eq.#2 from Eq.#1

  2 = 9a + 3b + c

-(5 = 4a + 2b + c)

 -3 = 5a + b    (Eq.#5)

 Subtract Eq#4 from Eq.#5

  -3 = 5a + b

-(1 = 3a + b)

  -4 = 2a

-2 = a  (Eq.#6)     Substitute a into Eq.#5

-3 = -10 + b

7 = b     Eq.#7     Substitute a and b into Eq.#3

4 = -2 + 7 + c

-1 = c

y = -2x² + 7x - 1     Whew!