SOLUTION: A quadratic equation is given by y=2x^2 - 6bx+3.What is the value of 'b' if the equation of the axis of symmetry is x=9 ? I think the answer is 6 but I really don't fully understan
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Question 118946: A quadratic equation is given by y=2x^2 - 6bx+3.What is the value of 'b' if the equation of the axis of symmetry is x=9 ? I think the answer is 6 but I really don't fully understand, can someone please explain this to me ?
Found 5 solutions by jim_thompson5910, stanbon, Earlsdon, josmiceli, scott8148:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the axis of symmetry, take the x coefficient and divide it by and negate it. Remember, for , the axis of symmetry is . So in our case, . Since the axis of symmetry is x=9, this means
Plug in x=9
Negate -6b
Multiply
Multiply both sides by 4
Divide both sides by 6
So our answer is . So you are correct.
If we plug in into , we get
Plug in b=6
Multiply
Now let's graph
So we can see that the axis of symmetry is x=9. So this verifies our answer.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A quadratic equation is given by y=2x^2 - 6bx+3.What is the value of 'b' if the equation of the axis of symmetry is x=9 ? I think the answer is 6 but I really don't fully understand, can someone please explain this to me ?
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In the general form of a quadratic. y = ax^2+bx+c,
the axis of symmetry is x = -b/2a Where "b" is the coefficient of the 2nd term.
In Your Problem, "b" = -6b
So -(-6b)/(2*2) = 9
3b/2 = 9
b = 6
-----------
Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Given , find the value of b if the axis of symmetry is x = 9.
The axis of symmetry of a quadratic equation is given by: .
The a and the b come from the general form of the equation:
Since you are given the axis of symmetry as , you can write:
Substituting a = 2 and b = -6b, and x = 9, you get:
Simplifying this:
Multiply both sides by 4.
Finally, divide both sides by 6.
...which matches your answer.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I always refer beck to the quadratic formula when
I have an axis of symmetry problem.The formula is:
This finds the x-intercepts (roots)
when the equation is in the form
You can rewrite this formula as:
Think about what this says. It says " The axis of symmetry
is at and the roots are equally spaced on
either side, one on the minus side and one on the plus side
In the given equation, ,
represents in the quadratic formula (I used "B" to avoid
confusion). is the other variable.
The problem tells me this axis of symmetry is at , so
solve for
answer
The equation turns out to be
I'll plot this
This shows the answer is OK
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
for a quadratic of the form ax^2+bx+c, the equation for the axis of symmetry is x=-b/2a
in this case 9=-(-6b)/(2*2) __ 36=6b __ 6=b
looking at the quadratic formula can help to clarify
___ the formula gives two solutions and
the average of the two solutions (which is the midline of the graph) is -b/2a
__ the square root portions cancel each other
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