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# Back to basics, how to draw quadratic functions? watch

1. Hi
I've totally forgot how to draw quadratic functions
what are the steps? How do you begin?

eg X^2-4x+8
2. For every function of x (x axis) put a number in and plot it for y (y axis)

Example x = 2
Y = 4
3. The shape of the curve would be a smiley face if the coefficient of x^2 is positive and a frowny face if it's negative. In your case, it's in a U shape.

Find where it intersects the co ordinate axes (when x is zero and y is zero). Use any quadratic method to work them out.

And finally, vertex. You need to complete the square to find it. After plotting these points, you can already sketch a quadratic.
4. Find where it meets the x axis (assuming the expression in the OP is equal to zero). The sign of the term tells you if it's a or shape. You can find the turning point using trial and error, differentiation or noting that the x value of the turning point is the midpoint between the two roots. Then substitute the x value into the equation to find the coordinate of the turning point.

Differentiation is the best method though as it applies to any differentiable function, not just quadratics.
5. (Original post by Philosophy&Econ)
x
Of course you could just plot every point and go from there, or as others have suggested differentiate to find the turning point.

However, it's much more sophisticated to complete the square.

For example:

This can be written as: or in general terms

Then, you can easily sketch the curve from this information. The minimum of is always 0, so we know that the lowest part of the curve will be at b on the y-axis. Then, to work out where the lowest point will be on the x-axis you use the information that will be at its smallest when . Therefore, the minimum point on the curve is . Using the fact that quadratics are symmetrical, it's then quite easy to draw.

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Updated: July 20, 2012
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