Question

What are the coordinates of the vertex of y = x2 - 2x - 7?

Answer 1

the vertex form of a parabola is

\[y = (x - h)^2 + k\]

so group your equation as

\[y = (x - 2x ) - 7\]

complete the square in x

Answer 2

I have no idea how to do it

Answer 3

oops should be

\[y = (x^2 -2x ) - 7\]

Answer 4

ok... a perfect square is

\[(x - a)^2 ~~~ or ~~~~(x + a)^2\]

your question is similar the the 1st one.

expanding it gives

\[(x - a)^2 = x^2 - 2ax + a^2\]

Answer 5

so looking at the 1st part of your problem

\[y = (x^2 - 2x ) \]

what do you think the value of a is.. when you compare

Answer 6

x^2?

Answer 7

look at

\[x^2 - 2ax + x^2 ~~~ and ~~~~ x^2 - 2x + ?\]

what do you think a is

Answer 8

7? i dont know

Answer 9

here is an alternate method, this is part of the general quadratic formula.

for a quadratic \[ax^2 + bx + c\]

the line of symmetry is

\[x = \frac{-b}{2a}\]

this is also the x value in the vertex.

so you have a = 1 and b = -2

what is the value of x...?

Answer 10

Complete the square!!! mwuahahahaha

Answer 11

1?

Answer 12

well we are at an alternate method that gives the same result

fabulous @jwilliams03

you know x = 1 is part of the vertex.

to find the y part, substitute x = 1 into the equation.

What do you get...?

Answer 13

1^2 - 2* 1 - 7 right?

Answer 14

Vertex form : \(y=(x-h)^2 +k\)

Your goal is to change \(y=x^2-2x-7\) to fit that form.\[y=(x^2-2x)-7\]\[y=\left(x^2-2x+1\right) -7+1\]When you simplify that you will get the same thing @campbell_st has gotten :)

this is just an alternate way!

Answer 15

yes... that's it, what is the value..?

Answer 16

-8

Answer 17

yes @Jhannybean that's how I started by @jwilliams03 stuggled with the concept

Answer 18

great so you know x = 1 and y = -8

that's the vertex

(1, -8)

to easy

Answer 19

Okay thanks!

Answer 20

I caught my mistake, it was meant to read \(y=\left(x^2-2x+1\right) -7-1\)