1. ## Polynomial

Hey, there are a few more questions i am strugling with.

2(i) Express 3x²+12x+7 in the form 3(x+a)² +b

I think its 3(x+2)²-5 is that right?

(ii) Hence write down the equation of the line of symmetry of the curve y=3x²+12x+7

Would appreciate the help!

Next one:

10(iv) Given that 24x+3y+2=0 is the equation of the tangent to the curve at the point (p,q), find p and q. (The curve is y=1/3x³-9x.)

2. Originally Posted by LoveDeathCab
Hey, there are a few more questions i am strugling with.

2(i) Express 3x²+12x+7 in the form 3(x+a)² +b

I think its 3(x+2)²-5 is that right?

We need to complete the square here, i hope that's what you did. perhaps you're not comfortable with it? if you have any questions, just ask away. anyway, here goes

3x^2 + 12x + 7 = 3(x^2 + 4x) + 7
......................= 3(x^2 + 4x + (2)^2 - (2)^2) + 7

......................= 3[(x + 2)^2 - 4] + 7
......................= 3(x + 2)^2 - 12 + 7
......................= 3(x + 2)^2 - 5

(ii) Hence write down the equation of the line of symmetry of the curve y=3x²+12x+7

Now a parabola is symmetric about it's vertex. and when a parabola is written in the form:
y = a(x - h)^2 + k
then the vertex is given by (h,k)

we have
3(x + 2)^2 - 5 so our vertex is at (-2,-5)
since this is a parabola with a vertical axis (opens up or down, in this case up) the line of symmetry is just x = -2

3. Originally Posted by Jhevon
......................= 3(x + 2)^2 - 12 + 7
......................= 3(x + 2)^2 - 4
Hey, is there a small mistake here? Should it be -5? -12+7=-5? Just wondering cause i got 3(x + 2)^2 - 5

Thanks

4. Originally Posted by LoveDeathCab
Hey, is there a small mistake here? Should it be -5? -12+7=-5? Just wondering cause i got 3(x + 2)^2 - 5

Thanks
Yes, you are correct, it should be -5