Find the coordinate of the turning point of the curve y = x^2 - 10x + 7, by completing the square

First, we need to complete the square. We take the first part of the equation ignoring the constant ( + 7).  

y = x2 - 10x , we want to change the form of this equation from  x2 + ax + (a/2)2  into ( x + a/2 )2

y = ( x - 5 )2 - 25, what we did here was half the 10, and turn it into  ( x - 5 )2  and we then subtracted the square of half of 10.

We then need to remember the constant + 7, so we add this back to the equation. y = ( x - 5 )2 - 25 + 7 = ( x - 5 )2 - 18.

The coordinate of the turning point is then ( 5, -18).

JP
Answered by James P. Maths tutor

9324 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

express (1+4(root7)) / (5+2(root7)) as a+b(root7), where a and b are integers


Differentiate y=ln(2x^2) with respect to x


Find the equation of the tangent to the unit circle when x=sqrt(3)/2 (in the first quadrant)


How can I determine the stationary points of a curve and their nature?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences