VCE Methods Question Thread!

[Azila2004]

Hello!

Can you use the discriminant when using square-root graphs?

For example, what is the value of k if y= x + k intersects y=x^1/2 - 1/4 twice? I found one part of the answer, but not the full answer (I found that k is smaller than 0, but larger than -1/4.

[S_R_K]

Hello!

Can you use the discriminant when using square-root graphs?

For example, what is the value of k if y= x + k intersects y=x^1/2 - 1/4 twice? I found one part of the answer, but not the full answer (I found that k is smaller than 0, but larger than -1/4.

You can, but you need to be aware of issues raised by the domain / range of the square root function, and because sometimes the quadratic equation you get will have extraneous solutions.

For example, consider finding all values of k such that the line y = –x + k intersects y = x^(1/2) once. Using the approach where you set up a quadratic equation and solve for when the discriminant is zero, this will give k = -1/4. But clearly y = -x - 1/4 does not intersect the graph of y = x^(1/2); in fact, any non-negative value for k gives one solution.

An option in this case is to solve for when the discriminant is positive, giving k > -1/4, but then discard any values of k that give a point of intersection not in the domain / range of the square root function.

[kat05]

Hi there,
Could someone please help me with 17d. I get that I have to find the derivative but somehow i am not getting the answer

[fun_jirachi]

Hey there!

Recall that for some function \(e^{f(x)}\), \(\frac{d}{dx} = f'(x) \times e^{f(x)} \). Here, we have the rate of decay being \(\frac{d}{dt} 2e^{-0.2t}\). Try applying this idea to the function, with \(f(t) = -0.2t\).

Hope this helps

[Geoo]

Hi, I am having trouble on how to work out taking the derivative of a truncus and hyperbola function by hand. I was wondering if someone could tell me the rule,
and if someone could do a step by step for this function.

And this:

[SS1314]

Hi, I am having trouble on how to work out taking the derivative of a truncus and hyperbola function by hand. I was wondering if someone could tell me the rule,
and if someone could do a step by step for this function.
(Image removed from quote.)
And this:
(Image removed from quote.)

You just use the normal power rule. You first need to convert the hyperbola and truncus into the suitable form, i.e. change it to 1/3 times x^(-2).

Hope this helps 

[HELPER2020]

https://www.youtube.com/watch?v=EiDo-7gMoGQ&feature=youtu.be

 

[S_R_K]

https://www.youtube.com/watch?v=EiDo-7gMoGQ&feature=youtu.be

 

Thanks for the video, but in the right hand column the second line of working should have a "dy/dx" on the LHS.

[SS1314]

Thanks for the video, but in the right hand column the second line of working should have a "dy/dx" on the LHS.

Yes the person who has made the video has made a mistake.

[Snow Leopard]

Hello, I'm trying to graph quartics but I think my CAS is rounding off values on the graph such as the Turning Point.
For example, when I graphed: y = x^4 + 27x on my CAS, I got (-1.89, -38.3) as my values for my Turning Point but in the question it says we have to round to 2 decimal places and the answer said that the Turning Point was: (-1.89, -38.27).

So I was wondering how do you not make your CAS round values on your graph.
Thanks in advance!

[S_R_K]

Hello, I'm trying to graph quartics but I think my CAS is rounding off values on the graph such as the Turning Point.
For example, when I graphed: y = x^4 + 27x on my CAS, I got (-1.89, -38.3) as my values for my Turning Point but in the question it says we have to round to 2 decimal places and the answer said that the Turning Point was: (-1.89, -38.27).

So I was wondering how do you not make your CAS round values on your graph.
Thanks in advance!

On a graph page on the TI, Menu -> Settings -> Display digits.

But if you want exact values, it's best to use a calculator page and use derivatives or the fmax/fmin commands for turning points.

[colline]

Hello, I'm trying to graph quartics but I think my CAS is rounding off values on the graph such as the Turning Point.
For example, when I graphed: y = x^4 + 27x on my CAS, I got (-1.89, -38.3) as my values for my Turning Point but in the question it says we have to round to 2 decimal places and the answer said that the Turning Point was: (-1.89, -38.27).

So I was wondering how do you not make your CAS round values on your graph.
Thanks in advance!

Hey Snow Leopard, if you want your answer in decimal places but your CAS is giving you less than you need (such as in this case when you need it to 2 dp but your CAS gives you to one), you can simply select the value (in your case, -38.3) and click the '+' button on your CAS, and it will give you more decimal places.

[Snow Leopard]

Hey Snow Leopard, if you want your answer in decimal places but your CAS is giving you less than you need (such as in this case when you need it to 2 dp but your CAS gives you to one), you can simply select the value (in your case, -38.3) and click the '+' button on your CAS, and it will give you more decimal places.

Thank you so much!!!
I'm also struggling with graphing these other quartics with E's in them:
For example, when I graphed this quartic: y = x^4 - 81x^2, my turning points where: (-6.36, -1.64E+3) and (6.36, -1.64E+3)
So how do I turn the weird values with an E in them into numbers/decimals?

[fun_jirachi]

Hey there!

E+3 is just a different shorthand for x10³. In general, for some E+a, it's the same thing as writing x10^a.

Hope this helps

[Snow Leopard]

Hey there!

E+3 is just a different shorthand for x10³. In general, for some E+a, it's the same thing as writing x10^a.

Hope this helps

Thank you, that makes a lot of sense now!!!