Partial preview of the text
Download AQA A LEVEL MATHS PURE and more Schemes and Mind Maps Mathematics in PDF only on Docsity!
When a > 0, a quadratic A quadratic function can be written in the form @x* + bx +c, where a, b graph looks like this, and care constants and a #0 A quadratic equation can be written in the general form ax* + bx +c=0 Curves of quadratic functions, y = ax* + bx + ¢, have the same general shape. The curve crosses the y-axis when x=0, and the curve cross Wikta'a <0yequiliialie the x-axis at any roots (or solutions) of the equation ax*+ bx+¢=0 graph looks like this. Quadratic curves are symmetrical about their vertex (the turning point). For @ > 0, this vertex is always a minimum point, and for a <0 this vertex is always a maximum point. > = ‘ 5 2 § i The quadratic equation 3x° — 20x —7 =0 has solutions x=—— and x=7 Sketch the curve of f(x) = 3x* — 20x — 7, showing where it crosses the axes. When x=0, y= (0)? - 20(0)-7=-7 @ I ing the y-intercept y The curve y= f(x) crosses the x-axis at the solutions to f(x) = 0 a Try it on your Activity calculator Find out how to sketch the You can sketch a curve ona curve y= 4x*—11x—30n your graphics calculator. graphics calculator. [] Algebra 1 Quadratic functions 
