Write x^2+4x-12 in the form (x+a)^2+b where 'a' and 'b' are constants to be determined.

This question is asking us to complete the square. To find the value of a we must halve the coefficient of x. So, in this question: a = 4/2 = 2. To find the value of b we take the constant at the end of the quadratic, -12, in this case and subtract a2 from it: x2+4x-12 = (x+2)2-12-(2)2 - our value of a = 2, and 22 = 4 so: (x+2)2-12-4 = (x+2)2-16. So, a = 2, and b = -16. To check if these 2 quadratics are equal we can simply expand (x+2)2-16 to get: x2+2x+2x+4-16 = x2+4x-12 so we know we have completed the square correctly.

FA
Answered by Fizza A. Maths tutor

8220 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you solve a set of three similatenous equations with three unknown variables?


John has 12 marbles. Sandra has 10 more marbles than Kathy. Kathy has 4 times as many marbles as John. How many marbles does Sandra have?


You are given a square which you are told has a total area of 100 squared centimetres. You are also told that one side of the square has dimension 4(3x + 2), and the other has dimension 8x - y. What are the values of x and y?


How do you complete the square? example: x^2 + 8x + 13=0


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning