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Math question please help

For the graph of:

2x² -7x – 15

What’s the equation of the line of symmetry of the graph?

While you answer this can show me step by step what you need to do:

Thanks

Reply 1

Knogle

x=1.75

Just differentiate the equation and you get dy/dx = 4x - 7

Equate that to 0, => 4x = -7, => x = 1.75.

The graph is quadratic, therefore symmetrical about its minimum point.

Reply 2

Excalibur

First divide by 2 so that the coefficient of x^2 is 1.

= 2(x^2 - 3.5x - 7.5)

Now complete the square:

= 2[(x+1.75)^2 - 7.5 - 1.75^2]
= 2[(x+1.75)^2 - 10.5625]
= 2(x+1.75)^2 - 21.125

This means that the minmum y value of this quadratic is at -21.125, and the x value which gives this min y is at 1.75. Thus your line of symmetry should be x=1.75

Reply 3

Knogle

Excalibur

My method's way simpler. :aetsch:

Attached is a graph if you need some help visualising this.

graph.JPG63.7KB

Reply 4

CalculusMan

Yes it is, but I think hellom is a GCSE student and differentiation isn't on the syllabus (atleast it wasn't when I did it)

Reply 5

Knogle

MrTrig

Yes it is, but I think hellom is a GCSE student and differentiation isn't on the syllabus (atleast it wasn't when I did it)

You're kidding? :eek:

I know integration isn't in the GCE 'O' level syllabus, but differentiation certainly is!

Reply 6

yusufu

Knogle

You're kidding? :eek:

I know integration isn't in the GCE 'O' level syllabus, but differentiation certainly is!

Not in the UK it isn't.

Reply 7

Knogle

YYYY

Not in the UK it isn't.

Right, okay. *restrains self from ranting about the different academic systems and their levels of difficulty*

To the OP: Disregard my method then, although you should keep in mind that there exists an alternative and simpler solution to your problem.

Reply 8

hellom

Yep I am a GCSE student ,so does anyone know the 'GCSE' method of working it out?

Thanks

Reply 9

CalculusMan

The one that Excalibur showed, completing the square.

Reply 10

danniella

Hello!

As someone doing GCSE and AS level exams this year (don't ask) I can assure you that differentiation is not on the Higher Level syllabus. Neither is integration. You'd have to complete the square on that question. (apparently if I tried to do that question by differentiating in my GCSE exam (and got the correct answer) I wouldn't actually get any marks.)

love danniella

Reply 11

Kolya

Another simple solution exists:

\huge 2x^2-7x-15

\huge (2x+3)(x-5)

\huge Roots: -\frac{3}{2}, 5

\huge 5+(-\frac{3}{2}) = \frac{7}{2})

\huge \frac{7}{2}/ 2 = \frac{7}{4}

\huge x = \frac{7}{4}

Reply 12

KAISER_MOLE

I prefer the completing the square method anyway, you don't have to assume any symmetry , you just find it in tandem with finding where it's at (yea, I know where the symmetry is at, init!)

Reply 13

Knogle

KAISER_MOLE

I prefer the completing the square method anyway, you don't have to assume any symmetry , you just find it in tandem with finding where it's at (yea, I know where the symmetry is at, init!)

You don't assume symmetry. You know it's symmetrical just by looking at the equation.

Reply 14

generalebriety

Knogle

You're kidding? :eek:

I know integration isn't in the GCE 'O' level syllabus, but differentiation certainly is!

What the hell are O-levels? :p:

GCSEs replaced O-levels (at least in the UK, I dunno where you live) years ago. And are a lot simpler, admittedly. But you do more of them I think. Differentiation is in C1, the first (and easiest) core maths module of the A-level syllabus, as is integration, since the two are viewed as complementary, like multiplication and division (even though I know they're not quite).

As said before, the easiest (GCSE) way to do it is as follows:

y = 2x² -7x - 15
= 2(x² - 3.5x - 7.5)
= 2[(x - 1.75)² - 1.75² - 7.5]
= 2[(x - 1.75)² - 10.5625]
= 2(x - 1.75)² - 21.125

Squaring something is independent of the sign. If you square -3 you get 9, just as you do if you square 3. In fact, squaring any real number (for GCSE, read "squaring any number") will give you 0 or more. So the smallest that (blahhh)² can be is 0. In this case, (blahhh) = (x - 1.75). When (blahhh)² = 0, y = -21.125 (try it). This will be the lowest point on the graph (because any other value of (blahhh) will give you something bigger) and therefore the axis of symmetry will pass through it.

So:

y = -21.125
2(x - 1.75)² - 21.125 = 21.125
2(x - 1.75)² = 0
(x - 1.75)² = 0
x - 1.75 = 0
x = 1.75.

There's your equation.

Sorry that was so drawn out, I don't know how good you are at maths, but I hope you understood that and know sensibly which bits you could do with leaving out in the real exam and don't start spewing ten pages of crap for three marks or something. :smile:

Reply 15

Knogle

generalebriety

What the hell are O-levels? :p:

Yeah, many Commonwealth countries (e.g. Sri Lanka, Singapore) still use the 'O' levels.

The average kid in Singapore does 8 subjects, and the brightest do 11. The poorest do 6.

Reply 16

generalebriety

KAISER_MOLE

I prefer the completing the square method anyway, you don't have to assume any symmetry , you just find it in tandem with finding where it's at (yea, I know where the symmetry is at, init!)

What exactly did you just say, in words?

Reply 17

generalebriety

Knogle

Yeah, many Commonwealth countries (e.g. Sri Lanka, Singapore) still use the 'O' levels.

The average kid in Singapore does 8 subjects, and the brightest do 11. The poorest do 6.