math
posted by Morie .
HELP Not great in these
Express y=2x^2 12x +23 in the form
y=2(xc)^2 + d
The graph of y=x^2 is transformed into the graph of y=2x^2  12x +23 by the transformation
a vertical stretch with scale factor k followed by,
A horizontal translation of p units followed by,
a vertical translation of q units
what are the values of k, p , and q
HELP PLEASE!

2x^2 12x +23=2*(x^26x+23/2)
(xa)^2= x^22ax+a^2
(x3)^2= x^22*3*x+3^2= x^26x+3^2
2*(x^26x+23/2)=
=2*(x^22*3*x +3^2+ 23/2 3^2)
=2(x^26x+3^2)+2*(23/2)2*(3^2)
=2*(x3)^2+232*9
=2*(x3)^2+2318
=2*(x3)^2 +5
Proof:
2*(x3)^2+5=2*(x^22*3*x+3^2)+5
=2*(x^26x+9)+5
=2x^212x+18+5=2x^212x+23
So:
2x^2 12x +23 = 2*(x3)^2 +5
a vertical stretch =2
a yintercept is a point where the graph of a function intersects with the yaxis
2*0^212*0+23=00+23=23
vertical translation = 23
Quadratic function have extreme point
for x=(b/2a)
In this case a=2 b=12
(b/2a)=[(12/(2*2]=(12/4)=12/4=3
2x^2 12x +23 = 2*(x3)^2 +5
k=2
p=3
q=23
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