maths HELP

Username123455

11

Unsure as to how are the coordinates calculated, the answer is (-4,-5)

(edited 1 year ago)

vertex maths question.png25.6KB

Reply 1

mqb2766

21

Original post by Username123455

Unsure as to how are the coordinates calculated, the answer is (-4,-5)

Just looking at the equation shoiuld give you some ideas? Any thoughts?

Edit, even if you subbed some values into the equation, you should be able to reason about the minimum point. So x=0, -2, -4, -6 say?

(edited 1 year ago)

Reply 2

Username123455

OP

11

Original post by mqb2766

Just looking at the equation shoiuld give you some ideas? Any thoughts?

Edit, even if you subbed some values into the equation, you should be able to reason about the minimum point. So x=0, -2, -4, -6 say?

You should equate the two equations of the modulus one negative and one positive to find the x value and then find the y value for that, but im unsure as to why you equate them.

Reply 3

catgirl18

15

Equate:

2|x+4|-5 = 2|-x-4|-5

2x + 8 - 5 = -2x - 8 - 5

2x + 3 = -2x - 13

4x = -16

x = -4

And then sub x = -4 into the y= equation and solve to find y which will give you y= -5

Coordinates are therefore (-4, -5)

Reply 4

catgirl18

15

Original post by Username123455

You should equate the two equations of the modulus one negative and one positive to find the x value and then find the y value for that, but im unsure as to why you equate them.

You equate the two equations because the point where they both meet, the coordinates will be the same, so essentially y=y and x=x
So basically you’re setting y=y and setting both equations equal to y.
It’s just a way of eliminating y I think, so your only unknown variable is x, like solving simultaneous equations to find x and y only it’s equations of graphs

Reply 5

mqb2766

21

Original post by Username123455

You should equate the two equations of the modulus one negative and one positive to find the x value and then find the y value for that, but im unsure as to why you equate them.

If you're finding the value of the function, you simply sub the value in. Have you tried?
You could equate the positive and negative of the modulus, but that would be overly complex?
The modulus satisfies
|.| >= 0
so the mimumum value of the function must be when the modulus is zero, so x = ...?
The question is very similar to a completed square form, except it uses the modulus instead of squaring. However the effect is similar. The minimum occurs when (.)^2 = 0 or |.| = 0. That gives the x and y values directly.

(edited 1 year ago)

Reply 6

Username123455

OP

11

Original post by mqb2766

If you're finding the value of the function, you simply sub the value in. Have you tried?
You could equate the positive and negative of the modulus, but that would be overly complex?
The modulus satisfies
|.| >= 0
so the mimumum value of the function must be when the modulus is zero, so x = ...?
The question is very similar to a completed square form, except it uses the modulus instead of squaring. However the effect is similar.

Thank you I do get it now, x=-4 when the modulus is 0 therefore y=-5.

Reply 7

mqb2766

21

Original post by Username123455

Thank you I do get it now, x=-4 when the modulus is 0 therefore y=-5.

Exactly. You can solve it algebraically, but its simply not necessary when the function is expressed like this.

Reply 8

catgirl18

15

Original post by mqb2766

If you're finding the value of the function, you simply sub the value in. Have you tried?
You could equate the positive and negative of the modulus, but that would be overly complex?
The modulus satisfies
|.| >= 0
so the mimumum value of the function must be when the modulus is zero, so x = ...?
The question is very similar to a completed square form, except it uses the modulus instead of squaring. However the effect is similar. The minimum occurs when (.)^2 = 0 or |.| = 0. That gives the x and y values directly.