Question

Find the vertex of the parabola whose equation is y = x^2 - 4x + 6.

Find the y-coordinate of the vertex of the parabola whose equation is y = x^2 - x + 2.

Answer 1

and once again, \[-\frac{b}{2a}\]

Answer 2

\[ y = x^2 - 4x + 6\]
\[a=1,b=-4\]

Answer 3

let me know what you get

Answer 4

you could always go full derp and use a graphing calculator but it is far easier to just use the formula

Answer 5

4/2 which is 2?

Answer 6

yes, right
that is the first coordinate of the vertex

Answer 7

whats the equation for the second coordinate?

Answer 8

second coordinate is
\[ y = 2^2 - 4\times 2 + 6\]

Answer 9

i.e. what you get for \(y\) when you replace \(x\) by the first coordinate

Answer 10

in this case it is \(y=4-8+6=-4+6=2\) so both the first and second coordinate of the vertex is \(2\) and the vertex is \((2,2)\)

Answer 11

is the y coordinate the first or second one in the parentheses?

Answer 12

Find the y-coordinate of the vertex of the parabola whose equation is \(y = x^2 - x + 2\) is a bit trickier because you have to work with fractions

Answer 13

the \(y\) coordinate is the second one
it goes \((x,y)\)

Answer 14

easy enough to remember because \(x\) comes before \(y\) in the alphabet

Answer 15

ah, then i think the answer is 1 and 3/4

Answer 16

for
\[y=x^2-x+2\]?

Answer 17

oh wait wait wait, is it 2 and 1/4?

Answer 18

not quite

Answer 19

2? -.-

Answer 20

it is still
\[-\frac{b}{2a}\] but in this case \(a=1,b=-1\) so the first coordinate of the vertex is \(\frac{1}{2}\) not \(2\) you had it upside down

Answer 21

the second coordinate takes some arithmetic
it is
\[y=\left(\frac{1}{2}\right)^2-\frac{1}{2}+2\]

Answer 22

which, if my arithmetic is correct, is
\[\frac{1}{4}-\frac{1}{2}+2=-\frac{1}{4}+2=\frac{7}{4}\]

Answer 23

wanna check it?

Answer 24

which is 1 and 3/4!

Answer 25

i knew that was the right answer!

Answer 26

hold the phone
it is \((\frac{1}{2},\frac{7}{4})\) which is not \((1,\frac{3}{4})\)

Answer 27

clear?

Answer 28

no, 7/4 = 1 and 3/4

Answer 29

i only need the y

Answer 30

right dad?

Answer 31

ooh i see what you are saying!!

Answer 32

yes dear
now don't stay out too late

Answer 33

lol! i wont, im just going to get pellet faced and be a whore!

Answer 34

lol

Answer 35

you done? or are there more

Answer 36

ill make a new post, and omg thanks for helping me so much dad!

Answer 37

yw dear