The vertex form of the equation of a parabola is y = 2(x + 3)2 - 5. What is the standard form of the equation?
A. x = 2y2 + 5y + 9
B. y = 2x2 + 5x + 9
C. y = 4x2 + 4x + 4
D. y = 2x2 + 12x + 13
Answers
(x+3)² = x(x+3) + 3(x+3) ⇒ x² + 3x + 3x + 9 = x² + 6x + 9
y = 2(x² + 6x + 9) - 5
y = 2x² + 12x + 18 - 5
y = 2x² + 12x + 13 This is the standard form of the equation. Choice D.
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Write and evaluate the expression. Then, complete the statements.ten less than the quotient of thirty and a numberEvaluate when t= 2A 2-column table with 5 rows. Column 1 is labeled Key Words with entries ten, less than, quotient, thirty, a number. Column 2 is labeled replace with entries 10, minus, divided by, 30, t.First, write the expression.Second,2 in for the variable, t.Third,by using.The answer is.
g(x) = x2 − 8x + 16
In which direction and by how many units should f(x) be shifted to obtain g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
Answers
Answer: The answer is (B) Right by 4 units.
Step-by-step explanation: The two functions f(x) and g(x) are defined as follows:
We are to check the correct transformation of the graph of f(x) to the graph of g(x).
We can rewrite the graph of g(x) as follows:
Comparing this with the equation of f(x), we can say that f(x) is shifted right by 4 units to obtain g(x).
The graphs of both the functions are shown in the attached figure.
Answer:
Left by 4 units
Step-by-step explanation:
I took it the first time and put Right 4 units and got it wrong. When i put left by 4 units i got it right.
Answers
Answer:
Answers
Answer: 2/3
Step-by-step explanation:
6 whole
Subtract the eaten fraction:
6 - denominator
2 - numerator
Thus,
6/6 - 2/6 = 4/6
Simplify: 4/6 = 2/3
Answer:
i think its 1/4
Step-by-step explanation:
Answers
Answer:
Step-by-step explanation:
5.22/6= 0.87 a piece
Answers
Answer:
x^2+4x+4=x(x−2)
Step-by-step explanation:
Answers
Answer:
First three terms = 28, 22, and 16
Step-by-step explanation:
The formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d, where:
- an is the nth term,
- a1 is the first term,
- n is the term position (e.g., 1st, 4th, etc.),
- and d is the common difference.
Step 1: Find a1:
We can find a1 by substituting 10 for an, 4 for n, and -6 for d in the nth term formula:
10 = a1 + (4 - 1) * -6
10 = a1 + 3 * -6
(10 = a1 - 18) + 18
28 = a1
Thus, the first term is 28.
Step 2: Find a2 (the second term):
Now, we can find the second term by substituting 28 for a1, 2 for n, and -6 for d in the nth term formula:
a2 = 28 + (2 - 1) * -6
a2 = 28 + 1 * -6
a2 = 28 - 6
a2 = 22
Thus, the second term is 22.
Step 3: Find a3 (the third term):
Now, we can find the third term by substituting 28 for a2, 3 for n, and -6 for d in the nth term formula:
a3 = 28 + (3 - 1) * -6
a3 = 28 + 2 * -6
a3 = 28 - 12
a3 = 16
Thus, the third term is 16.
Step 4: Write the first three terms:
Therefore, the first three terms of the arithmetic series are 28, 22, and 16.