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Week 8 in Precalc 11

This week in precalculus we analyzed the quadratic function. In the equation each letter/ variable represents something that can change the graph. The standard form or the vertex form is:

with this equation the variable “a” controls the expanding of the parabola. Meaning, it makes the graph skinny or wide. When y= $x^2$ The pattern for the graphs wideness is 1,3,5,7 or when a=1

when a>1 the graph slenders. For example: y= 5 $x^2$

when 0<a<1 the graph widens. For example: y= 0.5 $x^2$

And when a<0 or when it’s negative the graph reflects down meaning it opens downward for example: y= -2 $x^2$

The “P” in the equation represents the horizontal translation or slide if the number is negative it moves right and if it’s positive it moves left. For example: y= $(x-5)^2$ or y= $(x+5)^2$

The “q” of the equation represents the vertical translation. If it is positive it moves up, if it was negative it would move down. For example: y= $(x-4)^2$ +3 or y= $(x-4)^2$ -3