Question

Which of the following table of values is an example of a quadratic function

Answer 1

Answer:

y =  x² + 2  represent ( -2 , 6) , (-1,3) , (0 , 2) ,  (1 , 3) , (2 , 6)

y = (x - 1)²  represent (1 , 0) , (2,1) , (3 , 4) , (4 , 9) , (5 , 16)

Step-by-step explanation:

From the above question,

Quadratic Function f(x) = ax² + bx + c

Quadratic Equation ax² + bx + c = 0  where a, b and  c are real and a≠0

y =  ax² + bx + c

Substitute x = 0  and y = 2

2= 0 + 0  + c

=> c = 2

Hence y = ax² + bx + 2

Substitute x = -1 and x = 1  and y = 3

a - b + 2 = 3 =>  a - b = 1

a  + b + 2 = 3 => a + b = 1

on solving a = 1 and b = 0

Hence y =  x² + 2

Using similar procedure for other table

a + b + c = 0     Eq1

4a + 2b + c = 1    Eq2

9a + 3b + c = 4      Eq3

3a + b = 1       Eq2 - Eq1

5a + b  = 3       Eq3 - Eq2

a = 1  , b = - 2 , c = 1

y = x² - 2x + 1  

y = (x - 1)²

For more related question : https://brainly.in/question/10641249

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