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 :)
Answer:if A= [2 6] prove that (A')' = A
3 7
4 9
Step-by-step explanation:
Answer:
Total surface area = 73.56506
Step-by-step explanation:
I do not know what shape you are trying to find the total surface area for, but I hope this is correct & helpful.
Answer:
Step-by-step explanation:
From the graph we can see that
Diameter = 6 units
=> Radius = 3 units and centre is at (-3,7)
=> Equation is Circle with centre (-3,7) and radius of 3 units will be
Answer:
$ 2330
Step-by-step explanation:
a = $240
Earning at the end of fifth week = $ 680
increase in earnings per weak = ( 680 -240)/2 = 440/2 =110
d =110
l = a + (n-1)d
a20 = 240 + (19 * 110 ) = 240 + 2090 = 2330
