A curve (a) has equation, y = x^2 + 3x + 1. A line (b) has equation, y = 2x + 3. Show that the line and the curve intersect at 2 distinct points and find the points of intersection. Do not use a graphical method.

a) y = x2 + 3x + 1b) y = 2x + 3At points of intersection (a) = (b).2x + 3 = x 2 + 3x + 1Note this is a quadratic expression which will solve for 2 unique solutions, providing the discriminant (b2 - 4ac, where a, b and c are the coefficients ax2 + bx + c = 0) is greater than 0, thus proving that there are two distinct points of intersection.Solve for x.x 2 + x - 2=0x2 - 2x + x - 2 = 0x ( x - 2 ) + 1 ( x - 2 ) = 0x + 1 = 0 , x - 2 = 0x = (-1) , x = 2Sub values into (b) to solve for y.y = 2x + 3y = 2(-1) + 3 , y = 2(2) + 3y = 1 , y = 7Use values for x and y to express points of intersection as co-ordinates in the form (x,y)Points of intersection are;(-1,1) and (2,7).

Answered by Joseph C. Maths tutor

3707 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Richard wants to find out how often people buy crisps, a) name two things that are wrong with his survey question and b) create a better one


The range of a set of numbers is 15 1/4. The smallest number is –2 7/8. Work out the largest number.


How do I solve a quadratic equation?


Factorising and Expanding Brackets


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