Find the vertex of the Parabola?

Question

f(x)= 2x^2-4x+6

I'm so confused! Help?!

f(x)=2x^2-4x+6


I know the answer is (1,4) but how??

Answer 1

f(x)= 2x²-4x+6 ; f(x)=y

complete the square

y=2(x²-2x)+6

y=2[(x²-2x+1)-1]+6

y=2(x-1)²-2+6

y=2(x-1)²+4

vertex: (1, 4)

Answer 2

This has to do with an equation looking like this:
ax^2+bx+c
Look at your equation. see how a=2, b=-4 and c=6?
The equation for finding the vertex is -b/2a
Simply plug and chug.
-(-4)/2(2)
the answer is 1. This is the x value of the point which is the vertex.
Take this # and plug it into the origional equation to get the y value.
2x^2-4x+6
2(1)^2-4(1)+6
4
Therefore, at (1,4), the parabola changes from heading down to going up.
Hope that helped!

Answer 3

A parabola of the form y-ok = (x-h)^2 or y=(x-h)^2+ok has (h,ok) because the vertex. In all of your issues, the x-coordinate of the vertex is 0 as x^2=(x-0)^2 y=x^2 vertex(0,0) y=x^2+5 vertex (0.5) y=x^2-3 vertex (0,-3) y=x^2-2 vertex (0,-2) to finish the sq. x^2+4x, divide the coefficient of x via 2. (x+2)^2=x^2+4x+4 so, x^2+4x = (x+2)^2-4 (x^2-12x) similar concept. x^2-12x=(x-6)^2-36

Answer 4

I don't know what your background is in math, but there is a formulaic method of solving this problem, i.e., of finding the vertex of a quadratic equation.

Vertex of any quadratic equation is at the coordinates:
( -b/(2a) , f( -b/(2a) )

For the given equation: 2x^2 - 4x + 6,

a = 2, b = -4, c = 6, Thus,

-b/(2a) = 4/4 = 1

f( -b/(2a) ) = f(1) = 2 - 4 + 6 = 4

and finally,

( -b/(2a) , f( -b/(2a) ) = (1,4)

Answer 5

Easy way: Take the derivative, set equal to zero and solve:
4x-4=0
x=1,y=4
Harder way: Write f(x) in a(x-b)^2+c form:
2x^2-4x+6=2(x^2-2x)+6
=2(x^2-2x+1)+6-2
=2(x-1)^2+4
x=b=1, y=c=4

Answer 6

I think sending people to wikipedia is not answering a question but in this case there's a step by step explanation on how to solve a problem very similar to the one you have

Answer 7

you put this in your calculator...in y= if you have a TI-80 something.......and the vertex is the peak or the valley..so you trace the graph, or you can find it using a calc method...your answer would be the vertex lies at approx. (1,4) ..basically, when are you going to find your lowest point (if U shaped) or your highest point (if n shaped)

Answer 8

x = -b/2a = -(-4) / 2.2
= 4/4
= 1

f(x) = y
2.1^2-4.1 + 6 = 6

the vertex is (1,6)

Answer 9

wow i suck at math

Answer 10

-b/2a (1,4)