Question

y=x^2-6x+5=0 Find the vertex and write as an ordered pair.

Answer 1

@jim_thompson5910

Answer 2

You can find the vertex by finding the axis of symmetry, which can be found with this formula

x = -b/2a

This will help you find x. Once you have found your solution, plug in x into the original equation to find your y.

Answer 3

Do you know how to find a and b?

Answer 4

No

Answer 5

x=5, x=1 I believe this is the solution to the equation go to the link below for explanation...
http://www.quickmath.com/webMathematica3/quickmath/equations/solve/basic.jsp#c=solve_stepssolveequation&v1=x%5E2-6x%2B5%3D0&v2=x
just copy and paste into the url of a new tab and it should pop up
sammixboo will probably be more help than me, so trust her/his answers...

Answer 6

Well your original equation is set up in the form of
\(\tt{y = ax^2 + bx + c}\)

So now we know that a = 1 and b = -6!

Answer 7

@MAGENTAMA202 I want to learn how to find it, not just the answer.

Answer 8

ok

Answer 9

So we plug in our values for a and b into the axis of symmetry formula to find our x-coordinate for the vertex.
\(\tt{x = \dfrac{-b}{2a}}\)

\(\tt{x = \dfrac{6}{2(1)}}\)

Answer 10

I'm just going to watch how sammixboo solved it if thats cool
i havent spent much time on this type of questions before :)

Answer 11

It's OK ;) If any of you guys have any further questions, let me know.

Are you understanding everything so far, @Gokuporter

Answer 12

Yes

Answer 13

OK, so do you know what \(\tt{x = \dfrac{6}{2(1)}}\) equals?

Answer 14

x=-3

Answer 15

It's positive 3 :)
Now we have found our axis of symmetry, we have also found the x-coordinate of our vertex. TO find our y-coordinate we must plug in 3 as x into the original equation, like so:
\(\tt{y=3^2-6(3)+5}\)

Answer 16

And solve. Do you know what this equals?

Answer 17

y=-4

Answer 18

@sammixboo

Answer 19

Correct! So do you know what the vertex is?

Answer 20

(3,-4)

Answer 21

Right :)