Question

Y = x2 + 7x – 5 can be written in the form y = (x + a)2 + b. Find the value of a and the value of b.

Answer 1

`a = (7)/(2)` and
`b = (-69)/(4)`

Explanation:

Given

`y = x^2 + 7x - 5`

Required:

Write as:

`y = (x + a)^2 + b`

Determine the values of a and b

`y = x^2 + 7x - 5`

`y = (x + a)^2 + b`

Expand

`y = x^2 + 2ax + a^2 + b`

So, we have:

`y = x^2 + 2ax + a^2 + b`

`y = x^2 + 7x - 5`

By comparison:

`2ax = 7x`

`a^2 + b = -5`

Solve for x in:
`2ax = 7x`

`2a = 7`

Divide through by 2

`a = (7)/(2)`

Substitute
`a = (7)/(2)` in
`a^2 + b = -5`

`((7)/(2))^2 + b = -5`

`(49)/(4)+ b = -5`

Make b the subject

`b = -5 -(49)/(4)`

`b = (-20-49)/(4)`

`b = (-69)/(4)`