Question

Write each function in vertex form.
Y=2x^2+x

Y=-2x^2-4x+6

Y=x^2-2x-6

Answer 1

there are a couple of methods
but i use this it seems easier but you have to memorize

-b/2a this is from the form ax^2 + bx + c
so from the first equation
b=1 and a=2 so - 1/2(2) = -1/4 now we have x(x,?)
insert x back into the eqUATION
y=2(-1/4)^2+(-1/4)
y=2(1/16)-1/4=1/8-2/8=-1/8

so (-1/4,-1/8) is our x and y or our h and k because the vertex form is:
y = a(x - h)² + k so plug in our values

y=2(x+1/4)^2 + (-1/8) or
y=2(x+.25)^2 - .125

see graph

Answer 2

i have time i can show you another method on the second eq. and then you can pick a method and do the third.

this method we will complete the square
first lets factor out coefficient on a to get ax^2 + bx + c
Y=-2x^2-4x +6 coefficient is -2
so
y=-2(x^2 + 2x + ? ) +6
?=1 putting 1 here completes our square
y= -2((x+1)(x+1)) +6 so we have
y= -2(x+1)^2 ?? +6 notice that we added 1 to complete the square

here it gets tricky because to keep everything even we have to subtract 1 and it is not really 1 we have to remember the -2 coefficient so -2(1) is -2 we have to add 2 to keep the equation even.

so
y= -2(x+1)^2 +2 +6
y= -2(x+1)^2 +8

y = a(x - h)² + k our (h,k) is (-1,8)

check with the graph and

ok


you do 3)

hope this helps!!!