Hello,
g(x)=4096^x
g(0)=1
g(0.25)=(2^12)^1/4=2^(12/4)=2^3=8
g(0.50)=(2^12)^(1/2)=2^6=64
g(0.75)=(2^12)^(3/4)=2^9=512
g(1)=4096^1=4096
The generic equation of a parabola is:
f (x) = ax ^ 2 + bx + c
To verify the equation of the parabola you need three points:
f (x) = ax ^ 2 + bx + c
We choose the points:
(x, y) = (- 1,7)
7 = a (-1) ^ 2 + b (-1) + c
7 = a - b + c
(x, y) = (0,5)
5 = a (0) ^ 2 + b (0) + c
5 = c
(x, y) = (- 2,5)
5 = a (-2) ^ 2 + b (-2) + c
5 = 4a - 2b + c
We solve:
c = 5
5 = 4a - 2b + 5
7 = a - b + 5
Rewriting
b = 2a
a-b = 2
Substituting:
a-2a = 2
a = -2
b = -4
The equation of the parabola is:
f (x) = - 2x ^ 2 -4x + 5
Option B: The value of x is -16
Explanation:
Given that the equation 
We need to determine the value of x.
Let us substitute f(x) = 0, then we have,
Now, we shall determine the value of x.
The term 
can be written as 
Hence, we have,
Also, the term 
can be written as 
Thus, we have,
Applying the exponent rule, 
, we have,
If 
then 
Simplifying, we get,
Therefore, the value of x is -16
Hence, Option B is the correct answer.
The Average test score start = 100%
It increases by 10%:
100% = 1
10% = 0.10
1 x 0.10 = 0.1
1 + 0.1 = 1.1
It increases by another 15%
1.1 x 0.15 = 0.165
1.1 + 0.165 = 1.265
Remember to move the place value digit to the right two spaces to make it a percentage
126.5% increase is your answer
hope this helps
Age is the x values and height is the y values. In order to be a function, there can be no repeating x values...they all have to be different. You can have repeating y values, just not the x ones. So look at all the x columns (ages) and u will notice that the only one that does not have any repeating x values is Hal's results....no x's are the same and it is therefore, a function.
