Maths help pls (1 Viewer)

[ttrinix]

Could anyone help me to solve these questions:
1) What is the equation of the parabola that concaves down, does not cut the x-axis and has a vertex (-2, 4)
2)For what values is -k^2 +5k -6>0
3)Find the equation of the parabola that passes through the following points:
(1,12), (-1,12),(-2,0)


Thankyou

 

[speedofsound]

What.

It's holidays.

 

[ttrinix]

uh..yeh, i would still like help

 

[camomile.tea]

Could anyone help me to solve these questions:
1) What is the equation of the parabola that concaves down, does not cut the x-axis and has a vertex (-2, 4)
2)For what values is -k^2 +5k -6>0
3)Find the equation of the parabola that passes through the following points:
(1,12), (-1,12),(-2,0)


Thankyou

1. Maybe I'm misreading the question but if a parabola concaves down and doesn't cut the x axis, the y value of its vertex should be negative

2.
-k^2 + 5k -6 >0
k^2 - 5k + 6 <0
(k-3)(k-2)<0
Sketch concave up parabola cutting at 2 and 3 on number line
The area below 0 is between 2 and 3
so the answer is 2< k<3

3. let the equation be y = ax^2+ bx + c
Sub (1, 12) to eqn
a + b + c = 12 (1)
Sub (-1, 12) to eqn
a - b + c = 12 (2)
Sub (1, 12) to eqn
4a - 2b + c = 0 (3)

(1) - (2): 2b = 0
b = 0
Sub to (3): 4a + c = 0 (4)
(1) + (2): a + c = 12 (5)

(4) - (5): 3a = -12
a = -4
Sub to (5): c = 16

Sub in a = -4, b = 0, c = 16 to y = ax^2 + bx + c
Therefore eqn is y = -4x^2 + 16

Hope that was of help

 

[ttrinix]

thanks alot, i also think that the first question has no solution

 

[suzlee]

yeah for the first question, if the parabola concaves down and doesn't touch the x-axis, y value of the vertex should be a negative (below the x-axis)

 

[Kittikhun]

To be honest, I just gave up when I looked at the first line of your question. Never learnt parabolas. Did you guys learn parabolas in 5.3 Maths? We never got to it, neither, polynomials. You're one bunch of lucky people, I must say.

 

[suzlee]

I'm pretty sure polynomials are one of the "optional" topics. Our class never went into too much detail with logarithms topic... cos it's also an optional one

 

[TBK11]

my gosh i have never herd of any of these topics
so this is what 5.3 is like ehhhh
i was in 5.2 and the last thing i recall doin was Simple interest i=prt XD

 

[camomile.tea]

We've done a few of the options: logarithm, polynomials, circle geometry, functions etc. You'll learn them next year. They're very simple and easy to understand so you don't really need to learn them too early.

 

[h3ll h0und]

the options were logarithms and functions, polynomials and circle geometry....they were actually quite fun to do cuz the rest of the year we did really easy work i heard that they're supposed to giv u a taste of year 11/12. theyr in the prelim/HSC course as well i think.