Answer:
f(x) = 2(x + 4)² - 2
Step-by-step explanation:
Equation of quadratic function whose vertex is (h, k),
f(x) = a(x - h)² + k
Equation of the function with vertex (-4, -2) shown in the graph will be,
f(x) = a(x + 4)² - 2
This graph is passing through a point (-6, 6) also,
6 = a(-6 + 4)² - 2
6 + 2 = a(-2)²
a = = 2
Therefore, quadratic function is f(x) = 2(x + 4)² - 2
Given expression .
Let us simplify step by step with explaination.
Let us read the given expression.
could be read as a power 3 and whole power 2.
Because we have whole power 2 of a^3. That represents two factors of (a^3) is there. So, we could write two factors of a^3 as (a^3)(a^3).
So, first step is (a^3) (a^3).
Now, each of the factor has a^3.
That is read as a power 3, that is three factors of a.
So, we can write a^3 in expanded form as a*a*a.
For each a^3, we would write a*a*a.
We have two facrors of a^3 there.
So, (a^3)(a^3) could be written as (a*a*a)(a*a*a).
There are 3+3=6 factors of a's there.
So, we could rewrite (a*a*a)(a*a*a) as 6 power of a.
That is a^6.
Therefore, we got the steps :
(a^3)^2 = (a^3)(a^3) = (a*a*a)(a*a*a) = a^6.
