# A-level Mathematics/Edexcel/Core 1/Graphs and transformations

## Graphs[edit | edit source]

For C1 it is important to be able to draw graphs and labelling points of intersection between graphs, as well as axes intersection points i.e., where the graph crosses the x-axis and the y-axis. You must be familiar with the equation y = mx + c which is the equation for any straight line graph. For drawing a line graph, you must be able to put any linear equation into the above form and work out the gradient (m) and the y-intercept (+c) For example, the line y + x = 7, we must put it into the y = mx + c form, so we get y = -x + 7. From here we can see that the gradient is -1 and the line crosses the y axis at 7. We can substitute in anotehr x value, say 1, to get another y value (-1 + 7 = 6) so we have a gradient, -1, a y-intercept = 7, and a co-ordinate (-1,6) so now we can draw the line. To draw a quadratic graph, we must be familiar with factorizing (see relevant page) and from here we get the roots of the graph. The general shape for a quadratic is the parabola which is a U shape for a positive quadratic, and an upside-down U shape for a negative one. We can substitiue x = 0 into the equation of the quadratic to get the y-interecept.

## Transformations[edit | edit source]

There are 4 basic types of transformations y = f(x)+a - movement up by a units y = f(x-a) - movement along by a units (for f(x+a) it would be a movement along by -a units) y = af(x) - a vertical stretch of sf a y = f(ax) - a horizontal stretch of sf 1/a