1.
Which of the following functions is quadratic?
Correct Answer
B.
Explanation
The quadratic function is a polynomial function of degree 2. It can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants. The function y = 2x^2 + 3x - 1 is quadratic because it is a polynomial of degree 2 and can be written in the form f(x) = 2x^2 + 3x - 1.
2.
The vertex of this parabola shows that the __________ value of the function is _____.
Correct Answer
B. Maximum; 4
Explanation
The vertex of a parabola represents the highest or lowest point on the graph. In this case, the vertex is described as a maximum, indicating that the highest value of the function is represented by the vertex. The value of the function at this vertex is given as 4, meaning that the function reaches a maximum value of 4.
3.
Find the zeros of from its graph below.
Correct Answer
A. 2 and 6
Explanation
The graph of the given function intersects the x-axis at the points x=2 and x=6. These points are called the zeros of the function because they are the values of x for which the function equals zero. Therefore, the correct answer is 2 and 6.
4.
Find the axis of symmetry of the parabola with zeros .
Correct Answer
A.
5.
If you graph , the y-intercept would be ______.
Correct Answer
C. 3
Explanation
The y-intercept of a graph is the point where the graph intersects the y-axis. In this case, the correct answer is 3, indicating that the graph intersects the y-axis at the point (0, 3).
6.
Which of the following statements is always true?
Correct Answer
C. The highest power of the independent variable in a quadratic function is 2.
Explanation
The highest power of the independent variable in a quadratic function is always 2. This is because a quadratic function is defined by an equation of the form f(x) = ax^2 + bx + c, where the highest power of x is 2. The coefficient "a" determines the shape and direction of the parabola, and the values of "b" and "c" determine the position of the vertex and the y-intercept. Therefore, regardless of the specific values of a, b, and c, the highest power of the independent variable in a quadratic function will always be 2.
7.
Which of the following statements is never true?
Correct Answer
B. The graph of a quadratic function that has a maximum opens upward.
Explanation
The statement "The graph of a quadratic function that has a maximum opens upward" is never true because a quadratic function with a maximum point opens downward. A quadratic function that opens upward has a minimum point.
8.
Which of the following quadratic functions has a maximum?
Correct Answer
A.
Explanation
A quadratic function has a maximum if the coefficient of the x^2 term is negative. This is because the graph of a quadratic function with a negative coefficient of x^2 opens downwards, creating a concave shape. The highest point on the graph is the maximum. Therefore, the quadratic function with a negative coefficient of x^2 will have a maximum.
9.
Which of the following quadratic functions has a minimum?
Correct Answer
D.
Explanation
A quadratic function has a minimum when the coefficient of the squared term is positive. This is because the graph of a quadratic function with a positive coefficient opens upwards, creating a "U" shape, and the lowest point of the graph is the minimum. Therefore, any quadratic function with a positive coefficient for the squared term will have a minimum.
10.
Identify the vertex of the given parabola.
Correct Answer
A.
11.
Which function has zeros shown in the graph?
Correct Answer
C.
Explanation
The function that has zeros shown in the graph is the function that crosses the x-axis at those points. Zeros of a function are the values of x for which the function equals zero. In the graph, the points where the function intersects the x-axis are the zeros of the function. These points indicate the values of x where the function evaluates to zero.
12.
Which of the following functions has a graph with an axis of symmetry of ?
Correct Answer
D.
13.
Which of the following quadratic functions has a graph with a y-intercept of 3?
Correct Answer
A.
Explanation
A quadratic function in the form of y = ax^2 + bx + c will have a y-intercept when x = 0. Therefore, to find a quadratic function with a y-intercept of 3, we need to find a function where c = 3. Among the given options, the only function that satisfies this condition is y = x^2 - 2x + 3.
14.
What are the solutions to the equation?
Correct Answer
A.
15.
What are the x-intercepts of the graph of the quadratic function ?
Correct Answer
A.
16.
The vertex of this parabola shows that the __________ value of the function is _____.
Correct Answer
C. Minimum; -9
Explanation
The vertex of a parabola represents the highest or lowest point on the graph, depending on whether the parabola opens upward or downward. In this case, since the vertex is at a negative value (-9), it indicates that the function has a minimum value. Therefore, the correct answer is "minimum; -9."
17.
Find the axis of symmetry of the parabola with zeros -1 and 6
Correct Answer
C. X = 2.5
Explanation
The axis of symmetry of a parabola is the vertical line that passes through the vertex of the parabola. The vertex is the midpoint between the zeros of the parabola. In this case, the zeros are -1 and 6, so the midpoint is (6 + (-1))/2 = 5/2 = 2.5. Therefore, the axis of symmetry is x = 2.5.
18.
The vertex of a quadratic function is in the second quadrant. The related equation has no real solutions. Which of the following statements is true?
Correct Answer
B. The graph opens upward.
Explanation
If the vertex of a quadratic function is in the second quadrant, it means that the parabola opens upward. This is because the vertex is the lowest point on the graph, and if it is in the second quadrant, it must be above the x-axis. Since the parabola opens upward, it does not intersect the x-axis, indicating that the related equation has no real solutions. Therefore, the correct statement is "The graph opens upward."
19.
What are the solutions to the equation?
Correct Answer
A. X = -5, 2
Explanation
The given equation has two solutions, -5 and 2. This means that when x is equal to -5 or 2, the equation will hold true. Therefore, the correct answer is x = -5, 2.
20.
What are the solutions to the equation?
Correct Answer
D. X = -2, 2
Explanation
The equation has multiple solutions, which are x = -2 and x = 2. These values satisfy the equation and make it true.
21.
What are the solutions to the equation?
Correct Answer
A. X = -3, -2
Explanation
The given equation has multiple solutions for x. The solutions are x = -3 and x = -2. This means that when x is equal to -3 or -2, the equation is satisfied.