Struggling trying to graph and do this question help asap please

Question

Y=|2 (x-3)(x+1)|

 

thank you so much! 

Hate dealing with graphs , suck at them.

Answer 1

I have just the right temperament to enjoy drawing these things carefully.

 

Start by graphing, lightly, y = 2(x-3)(x+1).  It should be a parabola with

 

x-intercepts (3,0) and (-1,0),

y-intercept (0, 2(0-3)(0+1)) = (0, -6)

vertex ((3+-1)/2, 2((3+-1)/2-3)((3+-1)/2+1) = (1, 2(1-3)(1+1)) = (1, -8)

[1 is halfway between -1 and 3 on the x-axis, and -8 is its corresponding y-value on the parabola.]

 

To graph y = |2(x-3)(x+1)|, leave all the parts above the x-axis where they are 

[For example, the point (4, 10) becomes (4, |10|) remains (4, 10).]

and take all the parts below the x-axis and flip them.

[For example, the point (1, -8) becomes (1, |-8|) = (1, 8).]

 

Then darken those parts at or above the x-axis.  [It should be sort of a W shape.]