Question

Find the vertex of the graph of the function.

f(x) = 2x2 - 8x + 9

Answer 1

shouldnt they tell u wats x ?

Answer 2

nope, this is a function so x can be anything

start by writing parentheses around the first two terms

Answer 3

f(x) = (2x2 - 8x) + 9

then factor what's inside the parentheses

Answer 4

it is found right in the middle , on the intersection with the line of symmetry

Answer 5

Completing the Square -

f(x) = 2x^2 - 8x + 9 = 2(x^2 - 4x + ____) + 9 - 2(____)

Fill in the two blanks with the magic number. What is the magic number?

Think on this (a+b)^2 = a^2 + 2ab + b^2
We have a^2.
We have 2ab.
How do we find b^2?

Answer 6

, that x value

Answer 7

im sorry but im still lost

Answer 8

where do i start

Answer 9

the x value of the vertex point, is -b/(2*a) , the y value is the function f(x) at that x value

Answer 10

do you need to see how to arrive there, or you can just remember it

Answer 11

standard quadratic

y = a*x^2 + b*x + c

there is also a vertex form that includes the values of the coordinates of the vertex to read off

Answer 12

so -b/(2*a) is -8/4=-2

Answer 13

notice the standard form has all addition between terms,so some of the constant values are negative

f(x) = 2x2 - 8x + 9 = 2x^2 + (-8)x + 9

Answer 14

a = 2
b = -8
c = 9

-b/(2a) is then +8/4

Answer 15

oh so its 2

Answer 16

yes, then find what y is there to complete the point

Answer 17

x=2 is the line of symmetry for the graph

Answer 18

vertex at (2 , f(2) )

Answer 19

give me a second sorry

Answer 20

here is a short sorta summary if you want to read it
http://hotmath.com/hotmath_help/topics/vertex-of-a-parabola.html

Answer 21

ok so y will equal 1 right

Answer 22

or am i off

Answer 23

8 - 16 + 9

Answer 24

1

Answer 25

what tkhunny was doing above with completing the square, is to convert standard to vertex form, then you can read off (h,k) from that equation...

That is where the -b/(2*a) can also be seen , comparing coefficients from one form to the other

Answer 26

oh ok i see it now sorry many people put different method and threw me off lol