anonymous
  • anonymous
Quadratic stuff giving me chest pains ._.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
y = −3x2 − 12x − 14 y = 3x2 + 12x − 14 y = −3x2 + 12x − 14 y = 3x2 − 12x − 14 Please explain, I don't just want an answer
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jim_thompson5910
  • jim_thompson5910
what is the vertex of this parabola
anonymous
  • anonymous
I don't know, you mean plugging in the number so a= 3x & b=12x.... and putting it into formula or something? o.o

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jim_thompson5910
  • jim_thompson5910
no at this point I just want to know the point that's at the peak of the parabola
jim_thompson5910
  • jim_thompson5910
think of it as at the very top of the mountain
anonymous
  • anonymous
-2,-2?
jim_thompson5910
  • jim_thompson5910
in general, a parabola is in vertex form if you see it written like this y = a(x-h)^2 + k where a = deals with how stretched/compressed the graph is h = x coordinate of vertex k = y coordinate of vertex
jim_thompson5910
  • jim_thompson5910
so (h,k) is the vertex since (-2,-2) is the vertex in this specific case, we know that (h,k) = (-2,-2) which means h = -2 and k = -2
jim_thompson5910
  • jim_thompson5910
from here, you plug these two values into y = a(x-h)^2 + k to get... y = a(x - h)^2 + k y = a(x - (-2))^2 + (-2) y = a(x + 2))^2 - 2 with me so far?
anonymous
  • anonymous
Yes :)
anonymous
  • anonymous
y= ax + 2a ^2 - 2
jim_thompson5910
  • jim_thompson5910
now let's use another point on the parabola notice how the point (-1,-5) lies on the parabola this means we also know that x = -1 and y = -5
jim_thompson5910
  • jim_thompson5910
plug those values in, then solve for 'a', to get y = a(x + 2)^2 - 2 -5 = a(-1 + 2)^2 - 2 -5 = a(1)^2 - 2 -5 = a(1) - 2 -5 = a - 2 -5 + 2 = a -3 = a a = -3
jim_thompson5910
  • jim_thompson5910
So, y = a(x + 2)^2 - 2 turns into y = -3(x + 2)^2 - 2 which is the equation of the parabola in vertex form
jim_thompson5910
  • jim_thompson5910
what you do from here is expand, distribute, combine like terms and simplify y = -3(x + 2)^2 - 2 y = -3(x + 2)(x + 2) - 2 y = -3(x(x + 2)+2(x + 2)) - 2 y = -3(x^2 + 2x + 2x + 4) - 2 y = -3(x^2 + 4x + 4) - 2 y = -3x^2 - 12x - 12 - 2 y = -3x^2 - 12x - 14
anonymous
  • anonymous
okay...
jim_thompson5910
  • jim_thompson5910
it's probably a lot to take in, so just practice practice practice and it'll click better hopefully
anonymous
  • anonymous
I think I get it but when you spit the equation, doing FOIL it kind of threw me off
jim_thompson5910
  • jim_thompson5910
well that's what FOIL is you multiply each piece of each binomial with each other but you're better off breaking it up like I did because you can't use FOIL for something like (a+b)(c+d+e) but you can use the trick I used to break that up
jim_thompson5910
  • jim_thompson5910
so it's best to keep in mind that (a+b)(c+d) = a(c+d) + b(c+d)
anonymous
  • anonymous
thanks :)
jim_thompson5910
  • jim_thompson5910
you're welcome

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