Core 3 - Transformations question Watch
Where is the question from?
So from y=x^2 to y=(x+2)^2 is a translation parallel to the x axis since the +2 is inside the function.
From y=x^2 to y=(x+2)^2 -4 is a translation parallel to y axis as -4 is outside the function.
From y=x^2 to the k[(x+2)^2-4] is then a stretch of k. Hope this helps!!
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i) 2 left
Stretch of scale factor k parallel to the y axis
ii) f(x) = k(x+2)^2 - 4k so minimum is -4k when x = -2. So f must be greater than or equal to -4k.
iii) Sketch graph of |f(x)|, if there are 3 values for |f(x)| = 20 then it must touch the top of the maxima, which is now 4k. 4k = 20 so k = 5.
5x^2 + 20x = 20
5x^2 + 20x - 20 = 0
x^2 + 4x - 4 = 0
x = 2 + 2root2
x = 2 - 2root2
x = - 2 (from part ii)
Slap wrists guys - some spoilerification (is that a word?) would not go amiss.