What are the x- intercepts of y= 2(x-7) (x+2)
1 answer:
You might be interested in
Answer:
<em>The coordinates of the vertex are (-1,-4).</em>
Step-by-step explanation:
<u>Equation of the Quadratic Function </u>
The vertex form of the quadratic function has the following equation:
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
We are given the function:
We must transform the equation above by completing squares:
The first two terms can be completed to be the square of a binomial. Recall the identity:
Thus if we add and subtract 1:
Operating:
The trinomial in parentheses is a perfect square:
Adding 4:
Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).
The coordinates of the vertex are (-1,-4).
Hence, the functions that produce given sequence are:
f(n) = 2n + 1
f(n) = 2(n − 1) + 3
Further explanation:
We will put n=1,2,3,4,5 to find which functions give the given sequence
<u>f(n) = 2n − 1</u>
Putting values of n
This function doesn't generate the given sequence
<u>f(n) = 2n + 1</u>
Putting values of n
This function generates the given sequence.
<u>f(n) = 2(n − 1) − 3</u>
Putting values of n
This function doesn't generate the given sequence
<u>f(n) = 2(n − 1) + 3</u>
Putting values of n
Hence, the functions that produce given sequence are:
f(n) = 2n + 1
f(n) = 2(n − 1) + 3
Keywords: Functions, Sequence
Learn more about functions at:
#LearnwithBrainly