What is the line of symmetry for the parabola whose equation is y = 3x2 + 24x - 1?

x = -8

x = -6

x = -4

Question

What is the line of symmetry for the parabola whose equation is y = 3x2 + 24x - 1?



x = -8

x = -6

x = -4

anonymous · Answer

Again use 
$$\frac{ -b }{ -2a }$$ 

I didn't tell you that you were finding the line of symmetry for the last problem, but now I think its necessary. 

Like I told you previously a= the first value in the equation provided and b= the second, etc

imstuck · Answer

the line of symmetry is x = -4, and I will show you how to do that, ok?

imstuck · Answer

you need to complete the square on the x terms in order to get this into graphing form.  Rewrite like this:

imstuck · Answer

$$y=(3x ^{2}+24x)-1$$and you will factor out the 3 since you cannot complete a square until the leading coefficient is 1.  So now you have this:

imstuck · Answer

$$y=3(x ^{2}+8x)-1$$Take half the coefficient on the x term (8) which is 4, square it (16) and add it to the inside of the parenthesis to complete the square, like this:

imstuck · Answer

$$y=3(x ^{2}+8x+16-16)-1$$now move the -16 out of the parenthesis, but when you do, remember that when it is inside the parenthesis it is being multiplied by a 3, so it would look like this in application:

imstuck · Answer

$$y=3(x ^{2}+8x+16)+(-16)(3)(-1)$$

imstuck · Answer

now the parenthesis look like this because what's inside the parenthesis now is a perfect square binomial:

anonymous · Answer

@IMStuck  Now that I think about it, I only showed him how to find the vertex of the parabola. So, don't use the previous question for reference.  Also IMStuck, I've been waiting for a hour or so for a question that I  asked that I got the answer for, but am not sure if it is right. Mind helping out?

imstuck · Answer

$$y=3(x+4)^{2}+(-16)(3)(-1)$$

imstuck · Answer

my answer of -4 was correct; I forgot we were looking for the line of symmetry and was confusing it with another problem to find the y coordinate of the vertex. So -4 is still correct, and we wouldn't even have to go further with this unless we want to, because the line of symmetry is found on the x axis, and since the x coordinate of the parabola's vertex is -4, that is where the line of symmetry is.

imstuck · Answer

HOWEVER, continuing on with your problem the whole equation for that parabola in graphing form is this:$$y=(x+4)^{2}+48$$