How do you sketch a quadratic graph?

There are three things to think about when sketching a quadratic graph: whether its a 'u' or 'n' shape, where it cuts across the y axis and where it cuts across the x axis (if it does). Let's look at an example: y= -3x2 +x+10A minus sign before the x2 means it's a 'n' shape (like a sad face because it's negative) and if there wasn't a minus sign before the x2 , it would be a 'u' shape (happy face). The graph cuts through the y axis when the x co-ordinate is 0 so substitute x with zero and we get y=10 (our y-intercept). The x co-ordinates where the graph cuts across the x axis are called the roots. The roots occur when the y co-ordinates are 0 so substitute y for 0. This leaves us with the quadratic equation -3x2+x+10=0. Solve this equation to get the roots using completing the square, the quadratic formula or factorisation. This time we can factorise: (3x+5)(-x+2)=0. Hence the roots are -5/3 or 2. Now draw the graph: it's an 'n' shape that cuts across the y axis at 10 and the x axis at -5/3 and 2.

SP
Answered by Sita P. Maths tutor

3176 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

A fridge of height 2m and width 0.8m is tilted in a delivery van so that one edge rests on the edge of a table and another touches the ceiling, as shown in the diagram. The total height of the inside of the van is 1.5m. Find the height of the table.


Simply fully (3x^2 - 8x - 3) / 2x^2 - 6x


Make x the subject of the equation y=(2(1+x))/(3x-1)


A right-angle triangle has three sides (diagram would be included). Side A = 3cm; Side B = 7cm. What is the length of Side C (the hypotenuse)? Give your answer to 2 d.p.


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