factor to solve quadtatic equations
1. what are the coordinates of the vertex of the graph? is it maximum or ninimum?
A- (1,0); minimum
B- (0, 1); maximum
C- (0,1); minimum
D- (1,0); maximum
2.graph the function and identify the domain and range.
y=-0.5x^2
A- domain: (♾, ♾) range: [0, ♾)
B- domain: (♾, ♾) range: (-♾, 0]
C- domain: (-♾, ♾) range: [0, ♾)
D- domain: (-♾, ♾) range: (-♾, 0]
3. how is the graph of y=-2x^2-4 different from the graph of y=-2x^2?
A- it is shifted 4 units to the left
B- it is shifted 4 units up
C- it is shifted 4 units to the right
D- it is shifted 4 units down
4. graph the function. identify the vertex and axis of symmetry.
f(x)=-x^2-x+2
i don't know, i got D
5. graph the function. identify the vertex and axis of symmetry.
f(x)=-2x^2+4x+1
i don't know, i got D
6. what are the solutions of the equation x^2-4=0? use the graph of the related function
A- there are two solutions: -2 and 2.
B- there are two solutions +_ square root of 2
C- there are no real number solutions.
D- there are two solutions: -2 and 2.
7. solve the equation using square roots.
5x^2-45=0
A- -3, 3
B- -9, 9
C- -square root of 3, square root of 3
D- no real number solutions
8. solve the equation using the zero product property.
(x-9)(x+7)=0
A- 9, 7
B- -9, -7
C- -1, 1
D- 9, -7
9. for questions 9-10, what are the solutions of the equation?
z^2-6z-27=0
A- 3, 9
B- 3, -9
C- -3, 9
D- -3, -9
10. c^2-4c=0
A- 0, -4
B- 0, square root of 4
C- 0- 4
D- 1, -square root of 4
1. B
2. D
3. D
4. A
5. B
6. D
7. A
8. D
9. C
10. C
Here are some ideas that should help you get started.
#1 - no idea, since no graph
#2 - there are lots of online graphing sites which can help you. The vertex is at (0,0), so that should help you determine the range. The domain of ALL polynomials is (-∞,∞)
#3 - well, 4 is subtracted from each y-value, so the graph is shifted down by 4
#4 - I don't know how you got D, since you showed no choices. But
-x^2-x+2 = -(x+2)(x-1)
The vertex is always on the axis of symmetry, midway between the roots. In this case, that is at x = -1/2. So find y(-1/2) to locate the vertex.
#5 - use the quadratic formula to find the roots, as in #4, or recall that for y=ax^2+bx+c, the vertex lies at x = -b/2a
#6 - x^2-4 = (x-2)(x+2)
#7 5x^2-45=0
x^2 - 9 = 0
(x-3)(x+3) = 0
#8 the zero product property states that if ab=0 then either a=0 or b=0
So, you have either
x-9 = 0
or
x+7 = 0
#9 z^2-6z-27=0
(z-9)(z+3) = 0
#10 c(c-4) = 0
Anonymous is 100% correct
oobleck yess, get it☝
To solve quadratic equations, you can use various methods such as factoring, graphing, completing the square, or using the quadratic formula. Let's go through each question and explain how to solve them:
1. To find the coordinates of the vertex of the graph, you can use the formula x = -b / (2a) to find the x-coordinate, and then substitute this value into the equation to find the y-coordinate. The quadratic equation is not given, so we cannot solve it directly. However, from the answer choices, we can see that the vertex is either (1,0) or (0,1). The fact that it is a minimum suggests that the correct answer is A.
2. To graph the function y = -0.5x^2, you can create a table of values by assigning values to x and calculating the corresponding y values. The domain represents all possible x values, and the range represents all possible y values. For this particular function, x can take any value since it is not restricted. The range, however, is limited to y values less than or equal to 0. This means the correct answer is B.
3. The graph of y = -2x^2-4 is different from the graph of y = -2x^2 due to the constant term. The constant term shifts the graph vertically. In this case, the graph is shifted 4 units down because the constant term is negative. Therefore, the correct answer is D.
4. To identify the vertex and axis of symmetry for the function f(x) = -x^2-x+2, you can use the vertex formula x = -b / (2a) to find the x-coordinate of the vertex. Once you have the x-coordinate, substitute it into the equation to obtain the corresponding y-coordinate. The vertex represents the minimum or maximum point of the graph, and the axis of symmetry is a vertical line passing through the vertex. Without performing the calculations, it is not possible to determine the answer from the given options.
5. Similar to the previous question, you can find the vertex and axis of symmetry for the function f(x) = -2x^2+4x+1 using the vertex formula. Without performing the calculations, it is not possible to determine the answer from the given options.
6. To find the solutions of the equation x^2-4=0, you can set the equation equal to zero and factor it. In this case, you have a difference of squares, which can be factored as (x+2)(x-2)=0. The solutions are the values of x that make the equation true, which are x = -2 and x = 2. Therefore, the correct answer is A.
7. To solve the equation 5x^2-45=0 using square roots, you can isolate x^2 by adding 45 to both sides of the equation. This gives you 5x^2 = 45. Then, divide both sides by 5 to get x^2 = 9. Taking the square root of both sides, you have x = ±√9, which simplifies to x = ±3. Therefore, the correct answer is A.
8. To solve the equation (x-9)(x+7)=0 using the zero product property, you need to set each factor equal to zero and solve for x. This gives you two separate equations: x-9=0 and x+7=0. Solving these equations, you find x = 9 and x = -7. Therefore, the correct answer is A.
9. To solve the equation z^2-6z-27=0, you can factor the quadratic expression as (z-9)(z+3)=0. To find the solutions, set each factor equal to zero. Therefore, z - 9 = 0 gives z = 9, and z + 3 = 0 gives z = -3. The correct answer is C.
10. To solve the equation c^2-4c=0, factor the expression as c(c-4)=0. Set each factor equal to zero, which gives c = 0 and c - 4 = 0. Solving for c, you find c = 0 and c = 4. Therefore, the correct answer is D.