Home » What is the vertex of ## y= x^2 -9 – 8x##?

What is the vertex of ## y= x^2 -9 – 8x##?

##(4, -25)##
We are given ##y=x^2-9-8x##.
First I want to get this into standard form This is easy, we just need to reorder it to fit the ##ax^2+bx+c## form.
Now we have ##x^2-8x-9##. The easiest way to get a standard form into vertex form is by . The process of completing the square is making ##x^2-8x+ (blank)## a perfect square. We just need to find the value that completes that. First we take the middle term, ##-8x##, and divide it by 2 (so ##-8/2##, which is ##-4##). Then we square that answer, ##(-4)^2##, which is ##16##.
Now we plug in ##16## in to the equation to make a perfect square, right?
Well, let’s take a look at that: ##x^2-8x+16-9=y##. Now, look again. We can’t just add a random number on one side of an equation and not add it on the other side. What we do to one side we must do to the other. So now we have ##x^2-8x+16-9=y+16##.
After we did all this work, let’s make ##x^2-8x+16## into a perfect square, which looks like this ##(x-4)^2##. Replace ##x^2-8x+16## with it and we have ##(x-4)^2-9=y+16##. Now I don’t know about you, but I liked having ##y## isolated, so let’s get it alone by subtracting ##16## on both sides.
Now we’ve got ##(x-4)^2-9-16=y##, which we can simplify to ##(x-4)^2-25=y##.
Now this is in vertex form, and once we have that it’s very quick to find the vertex. This is vertex form,##y = a(x – color(red)(h))^2 color(blue)(+k)##, and the vertex from that is ##(color(red)(h, color(blue)(k)))##.
In the case of our equation we have ##y=(x-color(red)(4))^2color(blue)(-25)##, or ##(color(red)(4), color(blue)(-25))##.
PLEASE NOTE that ##(color(red)(h), k)## is the opposite of what it was in the equation!
example: ##y=(x+3)^2+3##, vertex is ##(color(red)(-)3,3)##.
So, the vertex is ##(4, -25)##, and we can check this by graphing the equation and finding the vertex, which is the highest or lowest point on the parabola.
graph{x^2-8x-9}
Looks like we got it right!! Nice job!

Save Time On Research and Writing
Hire a Pro to Write You a 100% Plagiarism-Free Paper.
Get My Paper
Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
Live Chat+1 763 309 4299EmailWhatsApp

We Can Handle your Online Class from as low as$100 per week