Question

Pure mathematicsssss

Answer 1

Answer:

(i) a = 2

   b = -1

   c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

$f(x) = 2(x^{2} -2x+\frac{1}{2})$  

Step 2: Use the complete square method.

$f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )$  

Step 3: Have it to $a(x+b)^{2} +c$

$f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1$

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