Vertex form is y=a(x-h)^2+k, so we can rearrange to that form...
y=3x^2-6x+2 subtract 2 from both sides
y-2=3x^2-6x divide both sides by 3
(y-2)/3=x^2-2x, halve the linear coefficient, square it, add it to both sides...in this case: (-2/2)^2=1 so
(y-2)/3+1=x^2-2x+1 now the right side is a perfect square
(y-2+3)/3=(x-1)^2
(y+1)/3=(x-1)^2 multiply both sides by 3
y+1=3(x-1)^2 subtract 1 from both sides
y=3(x-1)^2-1 so the vertex is:
(1, -1)
...
Now if you'd like you can commit to memory the vertex point for any parabola so you don't have to do the calculations like what we did above. The vertex of any quadratic (parabola), ax^2+bx+c is:
x= -b/(2a), y= (4ac-b^2)/(4a)
Then you will always be able to do a quick calculation of the vertex :)
Yes i believe they are correct
(hope you get a 100% :))
The rule is n-4;
163 - 4 = 159
159 - 4 = 155
155 - 4 = 151
151 - 4 = 147
A quick way to solve this is to mutliply 4 by 23 and subtract the product from the 1st term.
23 x 4 = 92
163 - 92 = 71
The 23rd term is 71.
I hope this helps!
Answer:
Step-by-step explanation:
.6(2k-3)=3(4k+5) foil
1.2K-1.8=12k+15 subtract 1.5k from both sides
-1.8=10.8k+15 subtract 15 from both sides
-16.8=10.8k divide by 10.8
k= -1.5
The new tea is 75% Earl Grey and 25% Orange Pekoe.
$4 / pound times 75% = $3
$2 / pound times 25% = $0.5
$3 + $0.5 = $3.50 / pound
600 pounds times 75% = 450 pounds of Earl Grey
600 pounds times 25% = 150 pounds of Orange Pekoe
