Question

Pure mathematicsssss

Answer 1

(i) a = 2

b = -1

c = -1

(ii) x= 1

Explanation:

Step 1: Factorise

`f(x) = 2(x^(2) -2x+(1)/(2))`

Step 2: Use the complete square method.

`f(x)=2(x^(2) -2x+((-2)/(2))^(2) + (1)/(2) - ((-2)/(2))^(2) )`

Step 3: Have it to
`a(x+b)^(2) +c`

`f(x)=2((x-1)^(2) -(1)/(2) )\\ = 2(x-1)^(2) -1`

Line of symmetry:

To find line of symmetry, we use -b/2a formula.

Based from
`2x^(2) -4x+1`:

a=2, b=-4

-b/2a = -(-4)/2(2) = 1