Rule for raising a power to a new power

1 answer:

5 0

The practical rule would be, times that number, by the result of the first time you multiplied the first number. But, it would all depend by how much your're raising the number by.

For example: $\boxed{4^6}$

We do, $(4*4*4*4*4*4)= \boxed{\bf{4^6}}= 4096$

But, once again, this was an example. This would show and illustrate the rule of "raising a power".

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a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola

Jet001 [13]

Answer:

The vertex form of the equation is $y = -\frac{1}{3}( x-1)^{2} +1$ .

Step-by-step explanation:

You will use the equation $y=a(x-h)^{2} +k$ to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get $y= a(x - 1)^{2} +1$ .

Then, we substitute the point as our x and y to get $-2 = 9a+1$ (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the $9a$ to get $9a = 3$ . Finally, divide by 9 on both sides to get $a=\frac{1}{3}$ .

Now, substitute your $a$ back into the equation to get y = $-\frac{1}{3}(x-1)^{2}+1$ .

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get $y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}$ .