Question

y = 2x squared + 5x -3 can be written in the form y= 2( x+a) squared + b . Find the value of a and the value of b.

Answer 1

General vertex form:

$y = m(x − a)² + b \: with \: vertex \: at \: (a, b)$

Given :

$y = 2x² + 5x - 3$

Extract "spread factor" m

$y = 2( x² + \frac{5}{2} x) - 3$

Complete the square

$y = 2(x² + \frac{5}{2}x + ( \frac{5}{4})²) - 3$

$- 2( \frac{5}{4})²$

Write as a squared binomial and simplify the constant

$y = 2(x + \frac{5}{4})² - 6 \frac{1}{8}$

Re-write to match signs of standard general form:

$y = 2(x - ( - \frac{5}{4}))² \: + ( - 6 \frac{1}{8})$