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

Answer:

$a = \frac{7}{2}$  and  $b = \frac{-69}{4}$

Step-by-step 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

$a = \frac{7}{2}$

Substitute $a = \frac{7}{2}$ in $a^2 + b = -5$

$(\frac{7}{2})^2 + b = -5$

$\frac{49}{4}+ b = -5$

Make b the subject

$b = -5 -\frac{49}{4}$

$b = \frac{-20-49}{4}$

$b = \frac{-69}{4}$