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:
3,4 for cups of hot cocoa
4 for marshmallows
Step-by-step explanation:
dfggdr
4 hours? i may be wrong
i did - 60 * 15
seems about right, since 50% would be 7.5 hours?
Answer:
see explanation
Step-by-step explanation:
The nth term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₅ is double a₇ , then
a₁ + 4d = 2(a₁ + 6d) , that is
a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )
4d = a₁ + 12d ( subtract 12d from both sides )
- 8d = a₁
The sum of n terms of an AP is
= 
[ 2a₁ + (n - 1)d ] , substitute values
= 
( 2(- 8d) + 16d)
= 8.5(- 16d + 16d)
= 8.5 × 0
= 0
Answer:
Step-by-step explanation:
Part A: You can only use Pythagorean's Theorem on a right triangle.
Part B: The side across from the right angle is the hypotenuse. It has a length of 15.
Part C: To find the missing side using Pythagorean's Theorem:
and
and
and
a = 10.20
