Y = -(x – 4)^2+3 Standard form
1 answer:
Answer:
Step-by-step explanation:
The standard form of a quadratic equation is:
so to rewrite the equation in this form we do the following steps:
First we apply the formula
so now the equation becomes,
now if we compare the equation that we got with our standard form it is in the exact format thus the value of a = -1 , b = 8 and c = -13
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Hi there!
The answer is
In this formula d represents the diameter.
We know that 2 times the radius equals the diameter, hence
Therefore we can replace the 2r in the original formula by d, and then we get the following:
The answer is
In this formula d represents the diameter.
We know that 2 times the radius equals the diameter, hence
Therefore we can replace the 2r in the original formula by d, and then we get the following:
The system is
i)
ii)
In the second equation, the bases are equal, so we make the exponents equal to set the equation:
5y-4=10x-4. This means that 5y=10x, that is y=2x.
So, we can substitute y with 2x in the first equation:
.
Multiplying the second fraction by 2/2 and -1 by 2x/2x, we have:
.
Since the denominators are all equal, we can only work with the numerators, setting the equation:
-12+8x-10x+12=-2x,
simplifying we get 0-2x=-2x, that is -2x=-2x, which is always true. (Here remember that x cannot be 0 since x was in the denominator).
This means that for any (x, y) such that y=2x, the system is satisfied.
We can check that the correct statements are:
3) The point (1, 2) is a solution. (Since we have y=2x).
6) The system has infinitely many solutions. (Since any pair (x, 2x) is a solution, except when x=0)
i)
ii)
In the second equation, the bases are equal, so we make the exponents equal to set the equation:
5y-4=10x-4. This means that 5y=10x, that is y=2x.
So, we can substitute y with 2x in the first equation:
Multiplying the second fraction by 2/2 and -1 by 2x/2x, we have:
Since the denominators are all equal, we can only work with the numerators, setting the equation:
-12+8x-10x+12=-2x,
simplifying we get 0-2x=-2x, that is -2x=-2x, which is always true. (Here remember that x cannot be 0 since x was in the denominator).
This means that for any (x, y) such that y=2x, the system is satisfied.
We can check that the correct statements are:
3) The point (1, 2) is a solution. (Since we have y=2x).
6) The system has infinitely many solutions. (Since any pair (x, 2x) is a solution, except when x=0)