Question

What is the value of the x-coordinate of the vertex of the function shown below?

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

I converted this over to standard form and I almost have it in vertex for, which is what I need it in to complete this, I'll post my work below, I just need help with one step...

Answer 1

yeah thats one way to work the x coordinate of vertex,
but there is a shortcut if you use symmetry :
`x coordinate of vertex = average of x intercepts`

Answer 2

f(x) = x^2 - 6x + 2x - 12
f(x) = x^2 - 4x - 12

y = (x - 6)(x + 2)

Because I pulled these from the equation, the equation is correct... Would the y just be equal to this?

How would yhu do it with the symmetry?

Answer 3

f(x) = x^2 - 4x - 12

looks good, convert it into vertex form

Answer 4

do you know how to complete the square ?

Answer 5

No, I don't. I haven't heard of completing a square...

Answer 6

have you heard of -b/2a ?

Answer 7

OH! Yea. I know how to do it. c:

Answer 8

Well you have it factorized, so you know the x intercepts, 6 and -2 by using the null-factor law. Parabolas are symmetrical, which means one side is the mirror-image of the other and that the x co-ordinate of the vertex is exactly half way between intercepts.

To find the midpoint, add the intercepts and half the sum, which is what @ganeshie8 said.

6-2=4, 4/2=2

Now to find the y co-ordinate, just plug it back into the original function.

Answer 9

good work it using -b/2a and see if it matches with the method described by ilr1,

please medal ilr1 for nice explanation :) i gave u medal already and don't like to remove...

Answer 10

Will do. c:
So, with x being 2, I plug it in... So then it would be
f(2) = (2 + 2)(2 - 6)
Then... I foil it? ...... Right?

Answer 11

>.< I confused myself.

Answer 12

f(x) = x^2 - 4x - 12

a = 1
b = -4

x coordinate of vertex = -b/2a = (--4 )/ 2(1) = 4/2 = 2

Answer 13

which is same as the value worked out by ilr1 using symmetry

Answer 14

Yea, I got that far. . . Wait, If I was to plug it into the original equation, would that be checking it.... So 2 is my final answer?

Answer 15

2 is the x coordinate of vertex and yes thats the final answer

Answer 16

if you want y coordinate, plugin x=2 in the equation

Answer 17

Oh! I see now. Thank yhu both so much for the help ^.^ I appreciate it.

Answer 18

np :)