# Thread: [SOLVED] Line of Symmetry of a Function

1. ## [SOLVED] Line of Symmetry of a Function

Q) The function f is defined by f : x → 2x^2 − 12x + 13 for 0 ≤ x ≤ A, where A is a constant

(i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.

(ii) State the value of A for which the graph of y = f(x) has a line of symmetry

(iii) When A has this value, find the range of f

My Attempt

$\displaystyle 2x^2-12x+13$

$\displaystyle 2(x-3)^2-5$

Now I have no clue on how to do (ii) which is linked with (iii). Will appreciated your help!

Thanks!

2. Originally Posted by unstopabl3
Q) The function f is defined by f : x → 2x2 − 12x + 13 for 0 ≤ x ≤ A, where A is a constant

(i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.

(ii) State the value of A for which the graph of y = f(x) has a line of symmetry

(iii) When A has this value, find the range of f

My Attempt

$\displaystyle 2x^2-12x+13$

$\displaystyle 2(x-3)^2-5$

Now I have no clue on how to do (ii) which is linked with (iii). Will appreciated your help!

Thanks!
Obviously, the axis of symmetry should be the line x=3. (You should see this if you plot the graph of this function.)
Therefore A=6. (If we exclude the degenerate case A=0.)

3. What values would we take to plot the graph of this manually (with no graphing calculators) function in the quickest possible way on a graph paper during a test or exam? Kindly do elaborate.

Thanks!

4. Originally Posted by unstopabl3
What values would we take to plot the graph of this manually (with no graphing calculators) function in the quickest possible way on a graph paper during a test or exam? Kindly do elaborate.

Thanks!
I guess you can sketch y=x^2 - it goes through (0,0),(1,1),(2,4) (and symmetrically on the left).
The graph of y=2*x^2 is similar, but all points are in the double height -- it goes through (0,0),(1,2),(2,8).
Your function is $\displaystyle 2(x-3)^2-5$ - so you simply have to move the graph of $\displaystyle y=2x^2$ 3 units to the right and 5 units lower.

(I hope I was able to express myself clearly despite not being native English speaker.)

5. Also I tried to get the range and I got y= -5 and y= 13. Is this correct?

Yes, I understood that, but wouldn't that take a lot of time (5-10 mins) for such a question which has 2-4 marks maximum.

Thanks!

6. Originally Posted by unstopabl3
Also I tried to get the range and I got y= -5 and y= 13. Is this correct?
Yes, the range is correct.

Originally Posted by unstopabl3
Yes, I understood that, but wouldn't that take a lot of time (5-10 mins) for such a question which has 2-4 marks maximum.

Thanks!
I am definitely not in the position to answer this question. However, the amount of time you spend with a question during a test depends on how much practice you have and whether you have done some similar exercises before. So I think it's good that you're working hard and you're learning things in this forum.

7. Yeah I guess you are right, I will practice graphing these kind of functions a bit more.
Thanks!

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# The function f is defined by f : x → 2x2 − 12x 13 for 0 ≤ x ≤ A, where A is a constant

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