Question

I have been stuck on this questions for like ever please help..
Which of the following is the vertex of the function? y = x² - 14x + 13
A. (1, 0)
B. (3, -20)
C. (5, -32)
D. (7, -36)

Answer 1

Which method are you supposed to be using to solve this problem? How to get the answer kind of depends on what level of math you're at.

Answer 2

Im in Algebra1B

Answer 3

Not sure which way they're teaching you at that point, maybe to write it in vertex form? Vertex form is \(y=a(x-h)^2+k\), does that look familiar?

Answer 4

Yeah kinda

Answer 5

Okay, well let's do it that way. An easy way to put an equation in vertex form is to complete the square. To do that, we take half of the b term, which is -7, then square it, to get 49. Then we add and subtract it, to get \(x^2-14x+49+13-49\), which we can then group together like this: \((x^2-14x+49)+(13-49)\), and then factor it into \((x-7)^2-36\). So, we now have it in the form \(y=a(x-h)^2+k\), with \(h=7\) and \(k=-36\). The vertex is always \((h,k)\), so in this case it's \((7,-36)\).

There's also a shortcut that you can use that is based on this method. From the original polynomial, you can find the \(x\)-term of the vertex by using the formula \(\dfrac{-b}{2a}\). In this case that will give you 7, and then you can plug 7 into the original equation to get the \(y\)-term.

Answer 6

Oh ok thank you have a great night Im headed off to bed I will be back on tomorrow for more help bye