What is the equation of this graphed line?
2 answers:
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Option a: add 3 to the previous term; 13, 16
Explanation:
The sequence is 1, 4, 7, 10, ....
We need to determine the next two terms of the sequence.
Hence to find the next two terms, first we shall find the common difference between every two terms.
Common difference between 1 and 4 =
Similarly, common difference between 4 and 7 =
Common difference between 7 and 10 =
Hence, the common difference is 3.
So, the next two terms will also have the same common difference 3.
To determine the next two terms, first we shall add 3 to the term 10, we get,
Similarly, adding 3 to the term 13, we get,
Thus, the sequence is 1, 4, 7, 10, 13, 16, .....
Thus, add 3 to the previous term; 13, 16
Hence, option a is the correct answer.
The point that is not included in the solution set for the inequality in the graph is (-1, 3).
<h3>How to explain the graph?</h3>In the information given, (h, k) is the vertex point. In the graph, the vertex point will be (1, 2). The equation will be:
y = a(x + 1)² + 2
By the point of the graph(0, 3) the value of a will be:
3 = a(0 - 1)² + 2
3 = a + 2
a = 3 - 2
a = 1
The equation this becomes:
y = 1(x - 1)² + 2.
y = x² - 2x + 1 + 2
y = x² - 2x + 3
Therefore, the point that is not included in the solution set for the inequality is (-1, 3).
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