In this topic we shall be exploring how to draw graphs. But before we do that let’s look at the different types of graphs that you can sketch. You must know these graphs by heart.
Linear GraphsThe graph shown above in the illustration is called a linear graph. Graphs of this form are drawn using an equation of the form y = mx+c Linear graphs are ever straight line graphs.
Quadratic GraphsA quadratic graph such as the one shown in above is made using an equation of the form y = ax²+bx+c It has a distinctive cup shape.
Cubic GraphsThe cubic graph has been shown in the illustration above. Cubic graphs are formed using the equation of the form y=ax3+bx²+d. Note the first term in the equation has a cubic power.
Reciprocal GraphsThe graph shown has a reciprocal curve. Graphs of this form are made using the equation of the form y = a/x. The graph appears to have two curves.
FactsHere we have the curve y=x²; Note that the above is the default graph of the quadratic equation, there has been nothing added to the equation or multiplied. And now here is the curve of y = x² – 10 (blue) together with the curve of y = x²-10 (red) The curves are the same except the blue curve has been moved down (transformed) by taking 10 off the y values. He we conclude that; Adding or subtracting values at the end of an equation moves the curve down or upwards by that amount (in the y-axis) This has been shown in the following animation; Here is another quadratic curve of y=x²; What happens when we multiply the equation, the following illustration shows the result. We can see that as we multiply the equation of y=x² with an increasing number the graph gets steeper or squashes inwards. We can conclude that; Multiplying an equation stretches the curve upwards. The curve appears to be squashed inwards
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