Y=a(x-h)^2+k
vertex form is basically completing the square
what you do is
for
y=ax^2+bx+c
1. isolate x terms
y=(ax^2+bx)+c
undistribute a
y=a(x^2+(b/a)x)+c
complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside
y=a(x^2+(b/a)x+(b^2)/(4a^2)-(b^2)/(4a^2))+c
complete square
too messy \
anyway
y=2x^2+24x+85
isolate
y=(2x^2+24x)+85
undistribute
y=2(x^2+12x)+85
1/2 of 12 is 6, 6^2=36
add neagtive and postivie isnde
y=2(x^2+12x+36-36)+85
complete perfect square
y=2((x+6)^2-36)+85
distribute
y=2(x+6)^2-72+85
y=2(x+6)^2+13
vertex form is
y=2(x+6)^2+13
It would be 31. 31 is a whole number. since 0.91 is close to 1. We would round it to 31 because of that.
Distribute the 4 into the parenthesis by multiplying the numbers by 4.
New expression is:
24m-28
]Answer:
79.5
Step-by-step explanation:
just multiply 13.25 by 6 :D hope that helps
Answer:
and
Step-by-step explanation:
The standard equation of a circle is 
where the coordinate (h,k) is the center of the circle.
Second Problem:
- We can start with the second problem which uses this info very easily.
- (h,k) in this problem is (-2,15) simply plug these into the equation.
. - We can also add the radius 3 and square it so it becomes 9. The equation.
- This simplifies to .
First Problem:
- The first problem takes a different approach it is not in standard form. But we can convert it to standard form by completing the square.
first subtract 37 from both sides so the equation is now 
.- by adding
to both the x and y portions of this equation you can complete the squares. 
and 
which equals 49 and 4. - Add 49 and 4 to both sides and the equation is now:
You can simplify the y and x portions of the equations into the perfect squares or factored form 
and 
. - Finally put the whole thing together. .
I hope this helps!
