Chapter Closure
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The general equation of a parabola is y=a(x-h)^2+k.
The general equation of a cubic function is y=a(x-h)^3+k.
The general equation of a hyperbola is y=a( 1x-h )+k.
y=- 0.25(x+3)^2-12
y=2(x+6)^3+1
y=1/x-2 -6
To translate and stretch a parabola, its usually the easiest to use its graphing form.
Graphing Form:& y= a(x-h)^2+k
Vertex:& (h,k)
Stretch Factor:& a
If we substitute h=- 3 and k=-12, we can translate the parent function of a quadratic by 12 units down and 3 units to the left.
Finally, we want to stretch the parabola by a factor of 0.25 and make it open downward. If a=0.25 in the graphing form, the parabola will stretch by a factor of 0.25. However, to make it open downward, the value of a must also be negative. With this information, we can write the function. Function:& y= -0.25(x+3)^2-12 Vertex:& (-3,-12) Stretch Factor:& -0.25 Let's show this final transformation.
This is a cubic function. This family of functions can generally be written as follows.