Find the vertex of the function given below.
y= 2x2 + 4x + 1

vertex is (-1,-1)

Step-by-step explanation:

2 ways

1. get into vertex form y=a(x-h)^2+k

2. use math hacks

1.

vertex is (h,k) in y=a(x-h)^2+k

complete square

y=(2x^2+4x)+1

y=2(x^2+2x)+1

y=2(x^2+2x+1-1)+1

y=2((x+1)^2-1)+1

y=2(x+1)^2-2+1

y=2(x+1)^2-1

y=2(x-(-1))^2+(-1)

vertex is (-1,-1)

2.hack way

in form y=ax^2+bx+c

x value of vvertex is -b/2a

given

y=2x^2+4x+1

b=4, a=2

xvaluevertex=-4/(2*2)

xvaluevertex=-4/4=-1

sub back to find y value

y=2(-1)^2+4(-1)+1

y=2(1)-4+1

y=2-4+1

y=-1

y value is -1

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950