SOLUTION: g(x) = x²+mx+b h(x) = g(x-2) Two quadratic functions g and h are defined by the equations above. If h(x) is symmetrical about the y axis, what must be the value of m?

Algebra ->  Functions -> SOLUTION: g(x) = x²+mx+b h(x) = g(x-2) Two quadratic functions g and h are defined by the equations above. If h(x) is symmetrical about the y axis, what must be the value of m?      Log On


   

Question 1202596: g(x) = x²+mx+b
h(x) = g(x-2)
Two quadratic functions g and h are defined by the equations above. If h(x) is symmetrical about the y axis, what must be the value of m?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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g(x) = x²+mx+b
h(x) = g(x-2)
Two quadratic functions g and h are defined by the equations above. If h(x) is symmetrical about the y axis, what must be the value of m?
~~~~~~~~~~~~~~~ 

h(x) = g(x-2) = (x-2)^2 + m*(x-2) + b = x^2 - 4x + 4 + mx - 2m + b = x^2 + (m-4)x + constant terms.


Since h(x) is symmetrical about the y-axis, it implies that m-4 = 0,
i.e. m= 4.    ANSWER

Solved. 

Another explanation, expressed in other words, is that the plot of h(x) 
is the plot of g(x) shifted 2 units right.


Since h(x) is symmetric about y-axis, it means that the symmetry line of g(x) 
is x= -2.

In turn, it means that m= 4 in the expression of g(x), giving the same answer/value for m.

Solved, with explanations.