Question

What are the coordinates of the vertex for f(x) = 2x2 + 4x + 9?
(−2, 4)
(−1, 7)
(1, 15)
(2, 9)

Answer 1

formula to find x coordinate of vertex \[\huge\rm x=\frac{ -b }{ 2a }\]

Answer 2

then substitute all x in f(x) equation for its value to find y-coordinate of vertex

Answer 3

what do i put for the a and b?

Answer 4

a=leading coefficient
b=middle term \[\huge\rm \color{reD}{A}x^2+\color{blue}{B}x+C=0\]

Answer 5

ok thank you

Answer 6

do i leave the negative sign in front of the b even when it's a positive?

Answer 7

yes b is positive
but negative is in the formula so that stays there

Answer 8

so it would be \[x=\frac{ -4 }{ 2(2)}\]?

Answer 9

yep right

Answer 10

so -4/4 and i would just divide it and it would come out as -1 right?

Answer 11

yes that's x-coordinate

Answer 12

how do i find the y-coordinate now?

Answer 13

now to find y -coordinate
substitute x for -1 \[\rm \color{reD}{x=-1}\]
\[\huge\rm 2\color{reD}{x}^2+4\color{red}{x}+9=0\]

Answer 14

so the y-coordinate would be 3?
(-1,3)?

Answer 15

mhm

Answer 16

when you take square of negative number you will get positive number

Answer 17

how do i do that

Answer 18

\[\huge\rm 2\color{reD}{(-1)}^2+4\color{red}{(-1)}+9=0\]
now solve
(-1)^2 is same as -1 times -1 = ?

Answer 19

so 1?

Answer 20

yes -1 times -1 = 1
(-1)^2=1
so solve \[\huge\rm 2\color{reD}{(1)}+4\color{red}{(-1)}+9=?\]

Answer 21

oh so (-1,7)

Answer 22

yep

Answer 23

could you help me out with another one

Answer 24

@Nnesha

Answer 25

i'll try

Answer 26

What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1?

f(x) = −one fourth (x − 5)2 + 1
f(x) = one fourth (x − 5)2 + 1
f(x) = −one fourth (x − 5)2
f(x) = one fourth (x − 5)2

Answer 27

@Nnesha ?

Answer 28

well not sure about this
need to review this stuff hmm

Answer 29

sorry

Answer 30

its fine. i got it Cx thank you tho !

Answer 31

np