Question

http://prntscr.com/ncbbed

Answer 1

@Vocaloid

Answer 2

@mhchen

Answer 3

@dude

Answer 4

You need to find the vertex so just do

\(\large \frac{-b}{2a}\)

Answer 5

whats b

Answer 6

and whats a

Answer 7

Boye, the general quadratic equation is written as

\(ax^2+bx+c\)

Answer 8

\[-\frac{ b }{ 2a }\]

Answer 9

Yeah

Answer 10

\[h(t) = -4.9t^{2} + 20 t+65\]
The maximum height is when
\[h'(t)=0\]
Here,
\[h'(t) = -9.8t+20\]
Solving for t
\[-9.8t+20=0\]
\[t=20/9.8 =2.04 s\]
The maximum height is
\[h(2.04) = -4.9*2.04^{2} + 20*2.04+65 = 85.4\]
The maximum height is =85.4m

Answer 11

Wow thank you @Narad

Answer 12

http://prntscr.com/nccgdp

Answer 13

@Narad what about this one^

Answer 14

Let the quadratic function be
\[y=a(x-h) +k\]
\[(h,k)\] is the vertex
and \[a\] is a constant \[(a \in \mathbb{R} )\]
(h,k )= (3,1)
Plugging those values
\[y=a(x-3)^{2}+1\]
As the roots are 2 and 4
\[a(2-3) ^{2}+1 =0\]
\[a+1=0\]
\[a= -1\]
The quadratic function is \[y=-1(x-3)^{2}+1 =-(x^2-6x+9) +1 =-x ^{2} + 6x-9+1 = -x ^{2} + 6x-8\]

Answer 15

Wow I appreciate it

Answer 16

http://prntscr.com/nccuiu

Answer 17

The first line of the last problem is\[y= a(x-h)^{2} +k\]

Answer 18

oh okay got it

Answer 19

Let the width of the deck be \[= x \] yard
Then,
\[(8+2x)(10+2x)=120\]
\[80+16x+20x+4x ^{2} = 120\]
\[4x ^{2}+36x+80-120=0\]
\[4x ^{2}+36x-40=0\]
Dividing by 4
\[x ^{2}+9x-10=0\]
Factorising
\[(x-1)(x+10) =0\]
\[x=1 \] or \[x=-10\]
Discard the negative value
The width of the deck is = 1 yard

Answer 20

got it

Answer 21

http://prntscr.com/ncd63v

Answer 22

The equation is
\[4x ^{2}-6x-4=0\]
Divide by 2
\[2x ^{2}-3x-2=0\]
You can factorise the expression or apply the formula
\[(2x+1)(x-2) =0\]
\[2x+1=0 => x=-1/2\]
\[x-2=0 => x=2\]
The solutions are \

Answer 23

what are the solutions?

Answer 24

x=-1/2
or
x=2

Answer 25

Okay that makes sense

Answer 26

http://prntscr.com/ncd8gl

Answer 27

\[2(x-5) +4=30\]
\[2x-10=30-4\]
\[2x-10=26\]
\[2x=26+10\]
\[2x=36\]
\[x=36/2=18\]

Answer 28

Okay last one:
http://prntscr.com/ncdbjz

Answer 29

The equation is
\[y=a(x-h)^{2}+k\]
\[(h, k) = (-1, -8)\]
\[y=a(x+1)^{2} -8\]
The roots are x=-3 or x=1
Plugging the first root
\[a(-3+1)^{2}-8=0\]
\[4a-8=0\]
\[a=8/4 =2\]
The equation is\[y=2(x+1)^{2}-8=2(x ^{2}+2x+1)-8 =2x ^{2}+4x-6\]

Answer 30

Okay thank you very much I appreciate it (:

Answer 31

You are welcome