Question

Y = x^2+ 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

see explanation

Explanation:

The equation of a parabola in vertex form is

y = (x - h)² + k (h, k) are the coordinates of the vertex

Given y = x² + 7x - 5

To express in vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )²

y = x² + 2(
`(7)/(2)` )x +
`(49)/(4)` -
`(49)/(4)` - 5

y = (x +
`(7)/(2)` )² -
`(49)/(4)` -
`(20)/(4)`

y = (x +
`(7)/(2)` )² -
`(69)/(4)`

Hence

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