After 14 days, how many total homework questions have been assigned
2 answers:
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The geometric sequence is
Explanation:
Given that the first term of the geometric sequence is 15
The fifth term of the sequence is
We need to find the 2nd, 3rd and 4th term of the geometric sequence.
To find these terms, we need to know the common difference.
The common difference can be determined using the formula,
where and
For , we have,
Simplifying, we have,
Thus, the common difference is
Now, we shall find the 2nd, 3rd and 4th terms by substituting in the formula
For
Thus, the 2nd term of the sequence is 9
For , we have,
Thus, the 3rd term of the sequence is
For , we have,
Thus, the 4th term of the sequence is
Therefore, the geometric sequence is
The quadratic function in vertex form is:
y = a(x - h)^2 + k
Where:
vertex = (h, k)
Axis of symmetry: x = h
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we have these definitions, we can substitute the given values into the vertex form to solve for “a”:
Use vertex = (-4, -1) and y-intercept, (0, 7):
7 = a(0+ 4)^2 - 1
7 = a(4)^2 - 1
7 = a(16) - 1
Add 1 to both sides:
7 + 1 = a(16) - 1 + 1
8 = 16a
Divide both sides by 16 to solve for “a”:
8/16 = 16a/16
1/2 = a
Since a = 1/2 (which is positive, implying that the parabola opens upward), and the vertex occurs at point (-4, -1) as the minimum point:
The quadratic equation in vertex form is:
y = 1/2(x + 4)^2 - 1
Please mark my answers as the Brainliest, if you find my explanations/solution helpful :)
y = a(x - h)^2 + k
Where:
vertex = (h, k)
Axis of symmetry: x = h
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we have these definitions, we can substitute the given values into the vertex form to solve for “a”:
Use vertex = (-4, -1) and y-intercept, (0, 7):
7 = a(0+ 4)^2 - 1
7 = a(4)^2 - 1
7 = a(16) - 1
Add 1 to both sides:
7 + 1 = a(16) - 1 + 1
8 = 16a
Divide both sides by 16 to solve for “a”:
8/16 = 16a/16
1/2 = a
Since a = 1/2 (which is positive, implying that the parabola opens upward), and the vertex occurs at point (-4, -1) as the minimum point:
The quadratic equation in vertex form is:
y = 1/2(x + 4)^2 - 1
Please mark my answers as the Brainliest, if you find my explanations/solution helpful :)