Question 1181592: the equations y=a(x-2)^2 + c and y=(2x-5)(x-b) have the same graphs. determine the value of b.
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Expand both expressions and equate the coefficients of the quadratic, linear, and constant terms.
a(x-2)^2+c = a(x^2-4x+4)+c = (a)x^2+(-4a)x+(4+c)
(2x-5)(x-b) = (2)x^2+(-5-2b)x+(5b)
So
(1) a = 2 coefficients of quadratic terms
(2) -4a = -5-2b coefficients of linear terms
(3) 4+c = 5b coefficients of constant terms
Substitute (1) in (2) to solve for b:
-4(2) = -5-2b
-8 = -5-2b
2b = 3
(4) b = 3/2
ANSWER: b = 3/2
You can finish solving for c to check the answer....
Substitute (4) in (3) to solve for c:
4+c = 5(3/2)
4+c = 15/2
c = 7/2
CHECK:
y = (a)x^2+(-4a)x+(4+c) = 2x^2-8x+15/2
y = (2)x^2+(-5-2b)x+(5b) = 2x^2-8x+15/2
Yes; the two equations are the same; the values we found for a, b, and c are correct.
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