Step-by-step explanation:
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
Answer:
381.70350741116 inches^3
Step-by-step explanation:
4/3 πr^3 = 4/3 x π x 4.5^3 = 381.70 inches ^3
Answer:
$870 in his bank account
Step-by-step explanation:
420 / 3 = 140
140 * 6 = 840
840 + 30 = 870
For simple integer factors as this one has, you want to find two values for the quadratic in the form ax^2+bx+c. Let the two values be j and k. These two values must satisfy two conditions.
jk=ac=10 and j+k=b=11, so j and k must be 1 and 10.
Now replace bx with jx and kx...
2x^2+x+10x+5 now factor 1st and 2nd pair of terms.
x(2x+1)+5(2x+1)
(x+5)(2x+1)
