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:
g=7.5
Step-by-step explanation:
2/3g=45
divide both sides by 2/3
g=7.5
or
g=7 1/2
Y= f(x)= ax+b
when x= -1, y= -1
-1= -a+b | * ( -1)
when x= -3, y=2
2= -3a+b
-3a+b= 2
a - b= 1
--------------
2a=3
a=3/2 is the slope
The correct question is
<span>Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation
</span>
see the picture in the attached figure N 1we know that
The formula for Sample Standard Deviation is indicated in the attached figure N2
in this problem
n=4 and Yuri had to divide in the formula by 3
therefore
the answer is Yuri divided by n instead of n -1
You write each fraction that is equivalent to a whole number like this 2/1, 3/1, 4/1 as 2 over 1 or 3 over 1 or 4 over 1