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: 9p - 1.5a
Step-by-step explanation:
Your maximum heart rate is about 220 minus your age. But it varies base on age category.
Target heart rate during moderate intensity activities is about 50-70% of maximum heart rate.
According to the question;
Target heart rate for
women = 1/2p(418-4a)
= 209p - 2a ....... (1)
men = 1/2p(400-a)
= 200p - 0.5a .......(2)
To find the difference between the target heart rates for a fit woman and a fit man, take equation 1 from equation 2
(209p - 2a) - (200p - 0.5a)
209p - 2a - 200p + 0.5a
9p -1.5a
Step-by-step explanation:
7 = √49
8 = √64
So any positive integer between 50 to 63, both inclusive, have a square root between 7 and 8.
I solved it this way , hope it’s correct ;)
Three ventilation fans, each working alone, can clear the smoke out of a room in 12 hours, 16 hours, and 24 hours respectively. How long would it...
