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 :)
X - the number of sandwiches
y - the number of soups
10 sandwiches were ordered. The answer is D.
A rational number is 5.3 . It's rational because it can be written as a fraction a/b
- that is 5 3/10 or 53/10.
An irrational number between the 2 values would be √29
Enter this into ur calculator and you'll get an answer like 5.385164807 but this number carries on beyond bounds and can't be written as a fraction a/b It is irrational.
Answer:
Step-by-step explanation:
Gradient of a line =( y2 - y1)/x2 - x1
From the question, x1=4,y1=-1,x2=1,y2=0.
Therefore, substitute for these values in the above formula
m = 0-(-1)/1-4
= 0+1/-3
= -1/3.
Therefore, y-y1/x-x1 = -1/3
y - y1 = -1/3(x - x1)
y - (-1) = -(x-x1)/3
y+1 = - (x - 4)/3
Multiply through by 3
3y+3= -x+4
3y +x=4-3
x+3y= 1
Therefore the answer is A.
