# [SOLVED] Line of Symmetry of a Function

• May 7th 2010, 08:17 AM
unstopabl3
[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!
• May 7th 2010, 08:42 AM
kompik
Quote:

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.)
• May 7th 2010, 10:59 AM
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!
• May 7th 2010, 11:04 AM
kompik
Quote:

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.)
• May 7th 2010, 11:09 AM
unstopabl3
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!
• May 7th 2010, 11:14 AM
kompik
Quote:

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.

Quote:

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.
• May 7th 2010, 11:22 AM
unstopabl3
Yeah I guess you are right, I will practice graphing these kind of functions a bit more.
Thanks!

P.S