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).
Answer:
a = [1 3 5 7 9] and b = [12 9 6 3 1]
Step-by-step explanation:
The addition of two vectors a and b is defined as
a + b = [13 12 11 10 10] .... (1)
The subtraction of two vectors a and b is defined as
a - b = [-11 - 6 - 1 4 8] .... (2)
After adding (1) and (2), we get
(a + b) + (a - b)= [13 12 11 10 10] + [-11 - 6 - 1 4 8]
On simplification we get
2a = [13-11 12-6 11-1 10+4 10+8]
2a = [2 6 10 14 18]
Divide both sides by 2.
a = [1 3 5 7 9]
Substitute the value of vector a in equation (1).
[1 3 5 7 9] + b = [13 12 11 10 10]
Subtract vector a from both sides.
b = [13 12 11 10 10] - [1 3 5 7 9]
On simplification we get
b = [13-1 12-3 11-5 10-7 10-9]
b = [12 9 6 3 1]
Therefore the vectors a and b are defined as a = [1 3 5 7 9] and b = [12 9 6 3 1].
Answer:
e
Step-by-step explanation:
Answer:
The Answer: 50°
Step-by-step explanation:
