The equation of a quadratic curve is y=x^2+ax+b. The points (6,-4) and (4,-6) lie on this curve. Find the co-ordinates of the turning point of the curve.

If y=x^2 + ax + b is the equation for the curve, then the points which lie on the curve must satisfy this equation.Inputing the points into the equation gives:-4 =6^2+6a+b -6=4^2+4a+bNow solve simultaneously to find a and b. Eliminate b by subtracting 2. from 1.1. - 2. : 2 = 20 +2a. Rearranging gives a = -9Substituting a =-9 into any of the equations gives b = =14. So the equation of the curve is y=x^2-9x+14. Completing the square to find the turning point gives: (x-(9/2))^2-(81/4)+14 which simplifies to (x-(9/2))^2-25/4. So co-ordinates of turning point is: (9/2,-25/4)

Answered by Sena A. Maths tutor

3681 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

rearrange c=(4-d)/(d+3)


Expand and simplify: (2x+3)(x-8)


How do I factorise a quadratic equation?


A bag contains only apple and oranges. The probability an apple is picked randomly is 1 in 5. The apple is returned, and five more apples are added to the bag. The probability of an apple being picked is now 1in 3. How many apples were there originally?


We're here to help

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