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Posted by **Morie** on Friday, December 10, 2010 at 5:18am.

Express y=2x^2 -12x +23 in the form

y=2(x-c)^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!

- math -
**Bosnian**, Friday, December 10, 2010 at 11:32am2x^2 -12x +23=2*(x^2-6x+23/2)

(x-a)^2= x^2-2ax+a^2

(x-3)^2= x^2-2*3*x+3^2= x^2-6x+3^2

2*(x^2-6x+23/2)=

=2*(x^2-2*3*x +3^2+ 23/2 -3^2)

=2(x^2-6x+3^2)+2*(23/2)-2*(3^2)

=2*(x-3)^2+23-2*9

=2*(x-3)^2+23-18

=2*(x-3)^2 +5

Proof:

2*(x-3)^2+5=2*(x^2-2*3*x+3^2)+5

=2*(x^2-6x+9)+5

=2x^2-12x+18+5=2x^2-12x+23

So:

2x^2 -12x +23 = 2*(x-3)^2 +5

a vertical stretch =2

a y-intercept is a point where the graph of a function intersects with the y-axis

2*0^2-12*0+23=0-0+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*(x-3)^2 +5

k=2

p=3

q=23

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