1.Solve the system of equations.
y = 2x^2 - 3
y = 3x - 1
a. no solution
b. (-1/2, 5), (2, -5/2)
c. (-1/2, -5/2), (2,5)
d. (1/2, 5/2), (2, 5)
2.how many real number solutions does the equation have 0 = -3x^2 + x - 4
a. 0
b. 1
c. 2
d. 3
3. solve the equation by completing the square. If necessary round to the nearest hundredth.
x^2 - 18x = 19
a. 1; 19
b. -1; 19
c. 3; 6
d. -3; 1
4. solve. x^2 - 81 = 0
a. 0
b. -9
c. -9, 9
d. 9
5. which model is most appropriate for the data shown in the graph below? (need wedsite to know the problem)
a. quadratic
b. linear
c. exponential
d. line
for questions 6-9, match the equation to its corresponding graph.
(need wedsite to know the problem)
a, b, c, d
6. y=-2x^2+2
7. y=-x^2
8. y=2x^2
9. y=3x^2-4
Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
(text box under question)
Here are the correct answers;
1. C (-1/2, -5/2), (2,5)
2. A 0
3. B -1;19
4. C -9,9
5. C Exponential
MATCHING
6. A
7. D
8. C
9. B
10. ESSAY
i know this is cheating but i need the answers please
For the essay question
10.Graph the quadratic functions y=-2x^2 and y=-2x^2+4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
Answer: The first function has a vortex at (0,0), while the second function has a vortex of (0,4). The difference between the two is that the second one is higher up on the y-axis than the first one, that it intercepts at a higher point than the first. They are the same without that difference. They both have the same shape too.
RO is 100% right. thanks RO :)
L Writeacher
y=3x+2
4x+2y=24
helppp
1. To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution:
Since both equations are equal to y, we can set them equal to each other:
2x^2 - 3 = 3x - 1
Rearrange the equation to have all the terms on one side:
2x^2 - 3x + 1 = 0
Now, we can solve this quadratic equation. You can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -3, and c = 1:
x = (-(-3) ± √((-3)^2 - 4(2)(1))) / (2(2))
Simplifying:
x = (3 ± √(9 - 8)) / 4
x = (3 ± √1) / 4
x = (3 ± 1) / 4
This gives us two possible x-values:
x1 = (3 + 1) / 4 = 4 / 4 = 1
x2 = (3 - 1) / 4 = 2 / 4 = 1/2
Now, substitute these x-values back into either of the original equations to find the corresponding y-values:
For x = 1:
y = 3(1) - 1 = 3 - 1 = 2
For x = 1/2:
y = 3(1/2) - 1 = 3/2 - 2/2 = 1/2
So, the system of equations has two solutions: (1, 2) and (1/2, 1/2).
Therefore, the correct answer is (d) (1/2, 5/2), (2, 5).
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2. To find the number of real number solutions for the equation 0 = -3x^2 + x - 4, we can determine the discriminant. The discriminant is calculated as b^2 - 4ac. If the discriminant is greater than 0, the equation has two real solutions. If the discriminant is equal to 0, the equation has one real solution. If the discriminant is less than 0, the equation has no real solutions.
For our equation, a = -3, b = 1, and c = -4:
Discriminant = (1)^2 - 4(-3)(-4)
Discriminant = 1 - 48
Discriminant = -47
Since the discriminant is less than 0, the equation 0 = -3x^2 + x - 4 has no real solutions.
Therefore, the correct answer is (a) 0.
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3. To solve the equation x^2 - 18x = 19 by completing the square, follow these steps:
1. Move the constant term to the right side of the equation:
x^2 - 18x - 19 = 0
2. Take half of the coefficient of the x term (-18/2 = -9) and square it:
(-9)^2 = 81
3. Add this squared value to both sides of the equation:
x^2 - 18x + 81 = 19 + 81
4. Simplify:
x^2 - 18x + 81 = 100
5. Rewrite the left side of the equation as a perfect square trinomial by factoring the squared term:
(x - 9)^2 = 100
6. Take the square root of both sides (remembering to consider both positive and negative square roots):
x - 9 = ±√100
7. Simplify:
x - 9 = ±10
8. Solve for x by adding 9 to both sides of the equation:
x = 9 ± 10
This gives us two possible values for x:
x1 = 9 + 10 = 19
x2 = 9 - 10 = -1
Therefore, the correct answer is (a) 1; 19.
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4. To solve the equation x^2 - 81 = 0, we can use the square root property:
1. Add 81 to both sides of the equation to isolate the squared term:
x^2 = 81
2. Take the square root of both sides, remembering to consider both positive and negative square roots:
x = ±√81
3. Simplify:
x = ±9
Therefore, the correct answer is (c) -9, 9.
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5. Without the accompanying graph, it is not possible to determine which model (quadratic, linear, exponential, or line) is most appropriate for the data shown.
Please provide the website or upload the graph for further analysis.
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Apologies, but I am unable to match equations to graphs or perform visual comparisons as I am a text-based AI.
I will not give you the answers, but tell you what you have to do
1. y = 2x^2 - 3
y = 3x - 1
both right sides are equal to y, so they must be equal to each other
2x^2 - 3 = 3x - 1
2x^2 - 3x - 2 = 0
this factors nicely
2.
0 = -3x^2 + x - 4
3x^2 - x + 4 = 0 , a=3, b= -1, c = 4
b^2 - 4ac = 1 - 4(3)(4) = -47
you would be dealing with √-47 which is not a real number, so what do you think?
3. x^2 - 18x = 19
take half of the -18, square that, and add it to both the left and the right side.
x^2 - 18x + 81 = 19 + 81
(x-9)^2 = 100
carry on
4. x^2 - 81 = 0
difference of squares ...
(x+9)(x-9) = 0
and the solutions are .....
5. ...... ?
Absolutely not!
But if YOU post what YOU THINK, someone might help you.