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).

JC
Answered by Joseph C. Maths tutor

4290 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

5 pencils cost 50p , how many would 2 pencils cost?


Solve ((x+2)/3x) + ((x-2)/2x) = 3


Work out 2(3/4)*1(5/7). Give your answer in mixed number form.


work out the area of a trapezium where the height is 4mm, the top length is 8mm and the bottom length is 12.5mm


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