Graphs, Need Help With A Question

[Scremin34Egl]

Hi, I am having trouble with question 4.6 of the question attached below. Has it got anything to do with equating the two graphs, maybe adding or multiplying them. I dont know what to do, Could someone maybe explain to me?

 

[Deleted member 4993]

Hi, I am having trouble with question 4.6 of the question attached below. Has it got anything to do with equating the two graphs, maybe adding or multiplying them. I dont know what to do, Could someone maybe explain to me?

Let

LM intersect the x-axis at N (O is the origin).

co-ordinate of L is (x₁,y₁)

co-ordinate of M is (x₁,y₂)

Then

y₁ = -1/2 * x₁ + 2 and

y₂ = x₁(x₁ + 3)

LM = y₁ - y₂ (why is sign of y₂ negative?) ........................................edit

Now what ......

 

[Scremin34Egl]

Let

LM intersect the x-axis at N (O is the origin).

co-ordinate of L is (x₁,y₁)

co-ordinate of M is (x₁,y₂)

Then

y₁ = -1/2 * x₁ + 2 and

y₂ = x₁(x₁ + 3)

LM = y₁ - y₂ (why is sign of y₂ negative?) ........................................edit

Now what ......

I think I understand what you are trying to say. LM,which is the length, is represented by the difference of the two y values which is represented by its equations and they obviously share the same x values. But I am having trouble getting it to look like the one in the question, heres what I tried,

LM = -1/2x +2 - (x^2 + 3x)
= -1/2x +2 - x^2 - 3x
= -x^2 - 7/2x + 2....................stuck

 

[Deleted member 4993]

I think I understand what you are trying to say. LM,which is the length, is represented by the difference of the two y values which is represented by its equations and they obviously share the same x values. But I am having trouble getting it to look like the one in the question, heres what I tried,

LM = -1/2x +2 - (x^2 + 3x)
= -1/2x +2 - x^2 - 3x
= -x^2 - 7/2x + 2....................stuck

Are familiar with a mathematical process called "completing square"?

 

[Scremin34Egl]

Are familiar with a mathematical process called "completing square"?

Yes, but dont know how im getting -81/16?

-x^2 - 7/2x +2
= -(x^2 + 7/2x -2)
= -(x^2 + 7/2x + 49/16) -2 -49/16
= -(x+7/4)^2 - 81/16

 

[Deleted member 4993]

Yes, but dont know how im getting -81/16?

-x^2 - 7/2x +2
= -(x^2 + 7/2x) + 2
= -(x^2 + 2*7/4 * x + 49/16) +2 +49/16
= -(x+7/4)^2 + 81/16

.