Express f(x) = x^2 + 5x + 9 in the form (x + a)^2 + b, stating the values of a and b.

The question asks you to complete the square on the function f(x). First, we split the function:

f(x) = (x^2 + 5x) + 9

And recognise that we need the form (x^2 + 2k + k^2). Identifying 2k = 5, we have that k = 5/2:

f(x) = (x^2 + 2*(5/2)x + (5/2)^2) + 9 - (5/2)^2

with the last term being due to the addition of (5/2)^2: completing the square. Resolving the expression:

f(x) = (x + 5/2)^2 + 11/4, with a = 5/2 and b = 11/4. Expanding the brackets again reforms the original expression.

LB
Answered by Lee B. Maths tutor

6551 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The graph of y = x^2 + 4x - 3 (Graph A) is translated by the vector (3 | 2), find the equation of the new graph (Graph B)


Find the value of x: x^2-3x-3=1


solve x^2 - x - 6 = 0


There are 10 boys and 20 girls in a class. The class has a test. The mean mark for all the class is 60. The mean mark for the girls is 54. Work out the mean mark for the boys.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences