Question
What type of equation will best fit the data below?
a coordinate plane with points plotted that form a U shape.
Responses
linear
quadratic
exponential
a coordinate plane with points plotted that form a U shape.
Responses
linear
quadratic
exponential
Answers
Answer
ty
Answer
Use the graph of f (x) to find the solutions to the equation f (x) = 0.
A coordinate plane with parabola opening up. The y-intercept is negative 12 and the x-intercepts are 2 and negative 6.
(1 point)
Responses
two solutions: x = 6, negative 2
two solutions: x = Image with alt text: 6, negative 2
two solutions: x = negative 6, 2
two solutions: x = Image with alt text: negative 6, 2
one solution: x = negative 12
one solution: x = Image with alt text: negative 12
no solutions
A coordinate plane with parabola opening up. The y-intercept is negative 12 and the x-intercepts are 2 and negative 6.
(1 point)
Responses
two solutions: x = 6, negative 2
two solutions: x = Image with alt text: 6, negative 2
two solutions: x = negative 6, 2
two solutions: x = Image with alt text: negative 6, 2
one solution: x = negative 12
one solution: x = Image with alt text: negative 12
no solutions
Answer
What are the solutions of the equation 2 x squared equals 2? Use a graph of a related function whose roots answer the question.
(1 point)
Responses
An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 1
Image with alt text: An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis. There are two solutions: Image with alt text: x equals plus or minus 1
An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 2
Image with alt text: An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis. There are two solutions: Image with alt text: x equals plus or minus 2
An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.
There are no solutions.
Image with alt text: An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis. There are no solutions.
An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: x equals plus or minus start root 2 end root
Image with alt text: An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis. There are two solutions: Image with alt text: x equals plus or minus start root 2 end root
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(1 point)
Responses
An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 1
Image with alt text: An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis. There are two solutions: Image with alt text: x equals plus or minus 1
An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 2
Image with alt text: An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis. There are two solutions: Image with alt text: x equals plus or minus 2
An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.
There are no solutions.
Image with alt text: An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis. There are no solutions.
An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: x equals plus or minus start root 2 end root
Image with alt text: An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis. There are two solutions: Image with alt text: x equals plus or minus start root 2 end root
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Answer
Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
(1 point)
Responses
10.35, 1.35
10.35, 1.35
10.35, negative 1 point 35
10.35, Image with alt text: negative 1 point 35
negative 10.35, negative 1.35
Image with alt text: negative 10.35, negative 1.35
negative 10.35, 1.35
Image with alt text: negative 10.35 , 1.35
x squared plus 9 x minus 14 equals 0
(1 point)
Responses
10.35, 1.35
10.35, 1.35
10.35, negative 1 point 35
10.35, Image with alt text: negative 1 point 35
negative 10.35, negative 1.35
Image with alt text: negative 10.35, negative 1.35
negative 10.35, 1.35
Image with alt text: negative 10.35 , 1.35
Answer
What is the simplified form of The quantity x to the fourth power minus 81 divided by the quantity x plus 3 ?
(1 point)
Responses
x cubed minus 3 times x squared plus 9 times x minus 27
Image with alt text: x cubed minus 3 times x squared plus 9 times x minus 27
the quantity x squared plus 9 times the quantity x squared minus 9
Image with alt text: the quantity x squared plus 9 times the quantity x squared minus 9
x cubed plus 3 times x squared plus 9 times x plus 27
Image with alt text: x cubed plus 3 times x squared plus 9 times x plus 27
x cubed plus 3 times x squared minus 9 times x minus 27
Image with alt text: x cubed plus 3 times x squared minus 9 times x minus 27
(1 point)
Responses
x cubed minus 3 times x squared plus 9 times x minus 27
Image with alt text: x cubed minus 3 times x squared plus 9 times x minus 27
the quantity x squared plus 9 times the quantity x squared minus 9
Image with alt text: the quantity x squared plus 9 times the quantity x squared minus 9
x cubed plus 3 times x squared plus 9 times x plus 27
Image with alt text: x cubed plus 3 times x squared plus 9 times x plus 27
x cubed plus 3 times x squared minus 9 times x minus 27
Image with alt text: x cubed plus 3 times x squared minus 9 times x minus 27
Answered by
GPT 3.5
The best type of equation that would fit the data described, which forms a U shape, is a quadratic equation.
Answered by
GPT 3.5
You're welcome! If you have any more questions, feel free to ask.
Answered by
GPT 3.5
We can see from the description that the parabola opens up, and it has x-intercepts at 2 and negative 6. Therefore, the solutions to the equation f(x) = 0 are two solutions: x = 2 and x = -6. Thus, the correct response is: two solutions: x = 2, -6.
Answered by
GPT 3.5
To find the solutions of the equation 2x^2 = 2, we can graph the related function y = 2x^2 - 2 and identify the x-intercepts.
The response that correctly describes the graph of the related function and the solutions is:
An upward facing parabola passes through points (-1, 0), (0, -1), and (1, 0).
There are two solutions: x = -1 and x = 1.
The response that correctly describes the graph of the related function and the solutions is:
An upward facing parabola passes through points (-1, 0), (0, -1), and (1, 0).
There are two solutions: x = -1 and x = 1.
Answered by
GPT 3.5
To solve the equation x^2 + 9x - 14 = 0 by completing the square, we follow these steps:
1. Move the constant term to the right side of the equation:
x^2 + 9x = 14
2. Take half of the coefficient of x (which is 9) and square it. Add this result to both sides of the equation:
x^2 + 9x + (9/2)^2 = 14 + (9/2)^2
x^2 + 9x + 81/4 = 14 + 81/4
3. Simplify both sides of the equation:
x^2 + 9x + 81/4 = 98/4 + 81/4
x^2 + 9x + 81/4 = 179/4
4. Rewrite the left side of the equation as a perfect square:
(x + 9/2)^2 = 179/4
5. Take the square root of both sides, considering both positive and negative square roots:
x + 9/2 = ±√(179/4)
6. Solve for x by isolating it on the left side:
x = -9/2 ± √(179/4)
The correct response is: x = -9/2 ± √(179/4), which can be approximated to x ≈ -10.35 and x ≈ 1.35.
1. Move the constant term to the right side of the equation:
x^2 + 9x = 14
2. Take half of the coefficient of x (which is 9) and square it. Add this result to both sides of the equation:
x^2 + 9x + (9/2)^2 = 14 + (9/2)^2
x^2 + 9x + 81/4 = 14 + 81/4
3. Simplify both sides of the equation:
x^2 + 9x + 81/4 = 98/4 + 81/4
x^2 + 9x + 81/4 = 179/4
4. Rewrite the left side of the equation as a perfect square:
(x + 9/2)^2 = 179/4
5. Take the square root of both sides, considering both positive and negative square roots:
x + 9/2 = ±√(179/4)
6. Solve for x by isolating it on the left side:
x = -9/2 ± √(179/4)
The correct response is: x = -9/2 ± √(179/4), which can be approximated to x ≈ -10.35 and x ≈ 1.35.
Answered by
GPT 3.5
To simplify the expression (x^4 - 81)/(x + 3), we can factor the numerator as the difference of squares:
(x^4 - 81) = (x^2)^2 - 9^2
= (x^2 - 9)(x^2 + 9)
Therefore, the simplified form of the expression is:
[(x^2 - 9)(x^2 + 9)] / (x + 3)
The correct response is: the quantity x squared minus 9 times the quantity x squared plus 9.
(x^4 - 81) = (x^2)^2 - 9^2
= (x^2 - 9)(x^2 + 9)
Therefore, the simplified form of the expression is:
[(x^2 - 9)(x^2 + 9)] / (x + 3)
The correct response is: the quantity x squared minus 9 times the quantity x squared plus 9.
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