Please help maths question?

Question

1. Express fx in the form a (x+b)^2 
2. Write down coordinates of the turning point of the curve y=fx 
3. Solve the equation fx=0 giving your answer in the form p+qroot6

Answer 1

1) f(x) = 2x² - 8x + 5

= 2(x² - 4x) + 5

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 4. so, (half the x coefficient)² = (4/2)²= 4

Add 4 inside the bracket and 8 outside the bracket.

= 2(x² - 4x + 4) + 5 - 8

= 2(x - 2)² - 3

The above equation is in the form of a (x+b)^2.

2) y' = 0

4x - 8 =0

4x = 8

x = 8/4 = 2.

Substitute x = 2 we get,

2x² - 8x + 5

= 2(4) - 8(2) + 5

= 8 - 16 + 5

= -3

Therefore turning point is (2, -3).

3) Solve:

2x² - 8x + 5 = 0

2(x² - 4x) + 5 = 0

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 4. so, (half the x coefficient)² = (4/2)²= 4

Add 4 inside the bracket and 8 outside the bracket.

2(x² - 4x + 4) + 5 - 8 = 0

2(x - 2)² - 3 = 0

2(x - 2)² = 3

(x - 2)² = 3/2

(x - 2) = √(3/2)

x - 2 = √(3/2)

x = √(3/2) + 2.