joshoyen
  • joshoyen
use the information provided to write the vertex form equation of each parabola. 1. y = -7x^2 - 14x - 6
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
SolomonZelman
  • SolomonZelman
factor the first two terms out of -7, please.
SolomonZelman
  • SolomonZelman
Note that: \(\color{#000000 }{ \displaystyle -7x^2=(-7)\cdot x^2 }\) and, \(\color{#000000 }{ \displaystyle -14x=(-7)\cdot 2x }\)
SolomonZelman
  • SolomonZelman
can you factor \(\color{#000000 }{ \displaystyle -7x^2-14x }\) out of -7?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

joshoyen
  • joshoyen
trying
SolomonZelman
  • SolomonZelman
sure ...
joshoyen
  • joshoyen
@SolomonZelman hm, im confused
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle ab+ac=a\cdot (b+c) }\) did you know?
joshoyen
  • joshoyen
Yeah I've seen the formula before but never really knew how to use it
SolomonZelman
  • SolomonZelman
Well, think about 2•4 + 8•4 = 4•(8+2) (factored out of 4) and in fact if you work both sides, 8 + 32 = 4 • (10) 40 = 40
SolomonZelman
  • SolomonZelman
So if you see two components that are both products, and both have some common term "a", then this "a" can be factored out like I did with "a" in the formla, and with "4" in the example.
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle -7x^2 - 14x}\) So wouldn't it make sense to say; \(\color{#000000 }{ \displaystyle (-7)\cdot x^2 + (-7)\cdot 2x}\) \(\color{#000000 }{ \displaystyle (-7)(x^2 +2x)}\)
joshoyen
  • joshoyen
ohhh okay i see now
SolomonZelman
  • SolomonZelman
So, \(\color{#000000 }{ \displaystyle y = -7x^2 - 14x - 6}\) \(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x)-6}\)
SolomonZelman
  • SolomonZelman
Ok, and do you know that: \(\color{#000000 }{ \displaystyle (x+a)^2=x^2+2ax+a^2}\) ?
joshoyen
  • joshoyen
hmm, no haven't seen that formula before
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle (x+a)^2=}\) \(\color{#000000 }{ \displaystyle (x+a) \cdot (x+a)=}\) \(\color{#000000 }{ \displaystyle x\cdot (x+a)+a\cdot (x+a)=}\) \(\color{#000000 }{ \displaystyle x\cdot x+x\cdot a+a\cdot x+a\cdot a=}\) \(\color{#000000 }{ \displaystyle x^2+xa+ax+a^2=}\) (xa is same as ax) \(\color{#000000 }{ \displaystyle x^2+2ax+a^2.}\)
SolomonZelman
  • SolomonZelman
I am doing a quick derivation of that...
SolomonZelman
  • SolomonZelman
you can look more into detail about \(\color{#000000 }{ \displaystyle x^2+2ax+a^2=(x+a)^2}\) but for know, you need to get \(x^2+2x\) into that form.
SolomonZelman
  • SolomonZelman
you can see that in our case "a" is? (Hint: 2ax in the formula coressponds to 2x in our case)
joshoyen
  • joshoyen
a is -7
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle x^2+2ax+a^2=(x+a)^2}\) \(x^2+2x\) 2x=2ax a=1
SolomonZelman
  • SolomonZelman
1²=1
SolomonZelman
  • SolomonZelman
So you need to add 1 to x²+2x to make it into the form of \(\color{#000000 }{ \displaystyle x^2+2ax+a^2~~~~~~~~~~~=(x+a)^2}\)
SolomonZelman
  • SolomonZelman
but we can't just add 1, because that changes the value however we can; \(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x)-6}\) \(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x+1-1)-6}\) The rule is: \(\color{#000000 }{ \displaystyle (A)(C-D)=AC-AD}\) (you can show this, you play with 5(5-3) = 5•5 - 5•3)
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x+1-1)-6}\) in our case \(\color{#000000 }{ \displaystyle x^2 +2x+1}\) is C and -1 is -D. (or [the last] 1 is D)
SolomonZelman
  • SolomonZelman
\(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x+1)-(-7)(1)-6}\) \(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x+1)+7-6}\) \(\color{#000000 }{ \displaystyle y=(-7)(x^2 +2x+1)+1}\)
SolomonZelman
  • SolomonZelman
notice that (x+1)²=x^2+2(1)(x)+1² = x² + 2x +1 so re-write the part in parenthesis.
SolomonZelman
  • SolomonZelman
and then the vertex of \(\color{#000000 }{ \displaystyle y=a(x-h)^2+k}\) is (h,k) and equivalent the vertex of \(\color{#000000 }{ \displaystyle y=a(x+t)^2+k}\) is (-t,k)
joshoyen
  • joshoyen
oh man thank you dude, i'm gonna have to read through all this again, i just can't get it
SolomonZelman
  • SolomonZelman
yes, and ask other people questions about anything you don't understand ... to ask is most important.
SolomonZelman
  • SolomonZelman
Good luck
whpalmer4
  • whpalmer4
Here's a slightly different approach: Your equation is a parabola: \[y = -7x^2 - 14x - 6\] If we have a parabola written in the form \[y = ax^2 + bx + c\]where \((a,b,c)\) are all constants as they are here (\(a=-7,\ b=-14,\ c=-6)\) we can find the vertex easily by knowing that the \(x\)-value of the vertex (which we will call \(h\)) will be\[x = -\frac{b}{2a}\]and the \(y\)-value (which we will call \(k\)) we get by just plugging the value of \(x\) into the formula of the parabola. Once you know the vertex is at \((h,k)\) you can write the formula for the parabola in vertex form using this: \[y = a(x-h)^2 + k\] The value of \(a\) is the same value we had for \(a\) when we found the vertex.

Looking for something else?

Not the answer you are looking for? Search for more explanations.