The parent function of these functions is y=x. Quadratic functions are easily recognized by an x. It doesn't necessarily have to be x, as long as there is a variable and the squared symbol. One example of a quadratic function would be y=x + 4x - 3. The graph of a quadratic function is a parabola, meaning it is u' shaped. The parabola can be oriented either upwards or downwards, and can face sideways, but that's a whole other paper(inverse functions, x=y). In order to plot this on a graph, you need it's roots, or where the graph crosses the x axis (x intercepts). In order to find the roots of this function, you use the quadratic formula.
x=-b b - 4ac. (y=ax + bx + c).
2a .
This is how the function y = x + 4x - 3 would break down:.
Step 1 x= -4 4 - 4(1)(-3) Step 2 x= -4 38.
2a 2a.
Step 3 X= -4 6.16 Step 4 x = 1.08.
2a x = -5.08 (origins) .
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If you want to be able to graph one of these equations by hand, you would need to put them in vertex form(y=[x+h] +k). The function y=x + 4x - 3, when put into vertex form would turn into y=(x+4) -- 3. Now you can plot your coordinates, which would be 4, 3.
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Absolute Value Functions:.
The parent function of these functions is y= |x|. These functions are easily recognized by the absolute value signs in the function( |x| ). These signs mean that the value is recognized by the distance x is from zero, not what x's written value. For example, the absolute value of 23 is 23, and the absolute value of -23 is also 23, because even though it's negative 23, it is still 23 units away from zero.
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