For question 3:
The graph of f(x) = 1/2x^2−2x is a parabola that opens upward. Using technology to graph the function, we can determine the following information:
A. The vertex and the y-intercept of f(x) are at the same point. - Not true. The vertex of the parabola is the lowest point on the graph, while the y-intercept is the point where the graph intersects the y-axis. In this case, the vertex of f(x) is (2, -2) and the y-intercept is (0, 0).
B. The two zeros of f(x) are at the same point - Not true. The zeros of f(x) are the points where the graph intersects the x-axis (y = 0). In this case, the zeros of f(x) are x = 0 and x = 4.
C. The vertex and one of the zeros of f(x) are at the same point. - Not true. As mentioned earlier, the vertex of f(x) is (2, -2) and the zeros of f(x) are x = 0 and x = 4.
D. The y-intercept and one of the zeros of f(x) are at the same point. - Not true. The y-intercept is (0, 0) and the zeros of f(x) are x = 0 and x = 4.
Therefore, none of the statements are true for question 3.
For question 4:
The graph of h(t) = −2t^2+6t−4 is a downward-opening parabola. Using technology to graph the function, we can determine the following information:
A. The vertex of h(t) is at (3/2, 1/2). - Not true. The vertex of the parabola is the highest point on the graph. In this case, the vertex of h(t) is (3/2, 5/2).
B. The two zeros of h(t) are at (−1, 0) and (−2, 0). - Not true. The zeros of h(t) are the points where the graph intersects the x-axis (y = 0). In this case, the zeros of h(t) are t = 1 and t = 2.
C. The y-intercept of h(t) is at (−4, 0). - Not true. The y-intercept is the point where the graph intersects the y-axis. In this case, the y-intercept of h(t) is (0, -4).
D. The axis of symmetry of h(t) is t=−3/2. - Not true. The axis of symmetry is a vertical line that passes through the vertex of the parabola. In this case, the axis of symmetry of h(t) is t = 3/2.
Therefore, none of the statements are true for question 4 either.
3. Use technology to graph the function f(x)=1/2x^2−2x . Then select the true statement below.
A. The vertex and the y-intercept of f(x) are at the same point.
B. The two zeros of f(x) are at the same point
C. The vertex and one of the zeros of f(x) are at the same point.
D. The y-intercept and one of the zeros of f(x) are at the same point.
4. The y-intercept and one of the zeros of f(x) are at the same point. h(t)=−2t^2+6t−4 where h is the height of the dolphin relative to the water level in meters at time t seconds. The graph of h(t) is given below. Then select the true statement.
A. The vertex of h(t) is at (3/2, 1/2) .
B. The two zeros of h(t) are at (−1, 0) and (−2, 0) .
C. The y-intercept of of h(t) is at (−4, 0) .
D. The axis of symmetry of h(t) is t=−3/2
3 answers
3. Use technology to graph the function f(x)=1/2x^2−2x . Then select the true statement below.
A. The vertex and the y-intercept of f(x) are at the same point.
B. The two zeros of f(x) are at the same point
C. The vertex and one of the zeros of f(x) are at the same point.
D. The y-intercept and one of the zeros of f(x) are at the same point.
4. The y-intercept and one of the zeros of f(x) are at the same point. h(t)=−2t^2+6t−4 where h is the height of the dolphin relative to the water level in meters at time t seconds. The graph of h(t) is given below. Then select the true statement.
A. The vertex of h(t) is at (3/2, 1/2) .
B. The two zeros of h(t) are at (−1, 0) and (−2, 0) .
C. The y-intercept of of h(t) is at (−4, 0) .
D. The axis of symmetry of h(t) is t=−3/2
A. The vertex and the y-intercept of f(x) are at the same point.
B. The two zeros of f(x) are at the same point
C. The vertex and one of the zeros of f(x) are at the same point.
D. The y-intercept and one of the zeros of f(x) are at the same point.
4. The y-intercept and one of the zeros of f(x) are at the same point. h(t)=−2t^2+6t−4 where h is the height of the dolphin relative to the water level in meters at time t seconds. The graph of h(t) is given below. Then select the true statement.
A. The vertex of h(t) is at (3/2, 1/2) .
B. The two zeros of h(t) are at (−1, 0) and (−2, 0) .
C. The y-intercept of of h(t) is at (−4, 0) .
D. The axis of symmetry of h(t) is t=−3/2
Apologies for the confusion, but I am unable to graph or view images. However, I can still provide some explanations to help you determine the true statements for each question.
For question 3:
To graph the function f(x) = 1/2x^2 - 2x, you can use technology like graphing calculators or graphing software to plot the points and observe the shape of the graph.
A. The statement "The vertex and the y-intercept of f(x) are at the same point" is not true. The vertex of a quadratic function, in this case, is (1, -3), and the y-intercept is (0, 0). They are different points.
B. The statement "The two zeros of f(x) are at the same point" is not true. The zeros, or x-intercepts, of f(x) occur when f(x) = 0. In this case, the zeros are x = 0 and x = 4, which are different points.
C. The statement "The vertex and one of the zeros of f(x) are at the same point" is not true. As mentioned above, the vertex is (1, -3), and the zeros are x = 0 and x = 4, which are different points.
D. The statement "The y-intercept and one of the zeros of f(x) are at the same point" is not true. The y-intercept is (0, 0), and the zeros are x = 0 and x = 4, which are different points.
Therefore, none of the statements are true for question 3.
For question 4:
Since I am unable to view the graph given, I can provide explanations to help you determine the true statement.
A. The statement "The vertex of h(t) is at (3/2, 1/2)" - To find the vertex of h(t) = -2t^2 + 6t - 4, you can determine the x-coordinate by using the formula x = -b/2a, where a = -2 and b = 6. The x-coordinate of the vertex is 1.5 (or 3/2), but we also need to find the y-coordinate. Substituting x = 1.5 into h(t) will give you the y-coordinate. Compare this to the given point to determine if it is true.
B. The statement "The two zeros of h(t) are at (-1, 0) and (-2, 0)" - To find the zeros of h(t), set h(t) = 0 and solve for t. Compare the solutions to the given points to determine if it is true.
C. The statement "The y-intercept of h(t) is at (-4, 0)" - To find the y-intercept of h(t), substitute t = 0 into h(t) and calculate the value. Compare this to the given point to determine if it is true.
D. The statement "The axis of symmetry of h(t) is t = -3/2" - The axis of symmetry of a quadratic function in the form h(t) = at^2 + bt + c is given by t = -b/2a. Compare this to the given equation to determine if it is true.
By analyzing the calculations and comparing the given points, you can determine which statement is true for question 4.
For question 3:
To graph the function f(x) = 1/2x^2 - 2x, you can use technology like graphing calculators or graphing software to plot the points and observe the shape of the graph.
A. The statement "The vertex and the y-intercept of f(x) are at the same point" is not true. The vertex of a quadratic function, in this case, is (1, -3), and the y-intercept is (0, 0). They are different points.
B. The statement "The two zeros of f(x) are at the same point" is not true. The zeros, or x-intercepts, of f(x) occur when f(x) = 0. In this case, the zeros are x = 0 and x = 4, which are different points.
C. The statement "The vertex and one of the zeros of f(x) are at the same point" is not true. As mentioned above, the vertex is (1, -3), and the zeros are x = 0 and x = 4, which are different points.
D. The statement "The y-intercept and one of the zeros of f(x) are at the same point" is not true. The y-intercept is (0, 0), and the zeros are x = 0 and x = 4, which are different points.
Therefore, none of the statements are true for question 3.
For question 4:
Since I am unable to view the graph given, I can provide explanations to help you determine the true statement.
A. The statement "The vertex of h(t) is at (3/2, 1/2)" - To find the vertex of h(t) = -2t^2 + 6t - 4, you can determine the x-coordinate by using the formula x = -b/2a, where a = -2 and b = 6. The x-coordinate of the vertex is 1.5 (or 3/2), but we also need to find the y-coordinate. Substituting x = 1.5 into h(t) will give you the y-coordinate. Compare this to the given point to determine if it is true.
B. The statement "The two zeros of h(t) are at (-1, 0) and (-2, 0)" - To find the zeros of h(t), set h(t) = 0 and solve for t. Compare the solutions to the given points to determine if it is true.
C. The statement "The y-intercept of h(t) is at (-4, 0)" - To find the y-intercept of h(t), substitute t = 0 into h(t) and calculate the value. Compare this to the given point to determine if it is true.
D. The statement "The axis of symmetry of h(t) is t = -3/2" - The axis of symmetry of a quadratic function in the form h(t) = at^2 + bt + c is given by t = -b/2a. Compare this to the given equation to determine if it is true.
By analyzing the calculations and comparing the given points, you can determine which statement is true for question 4.
1 answer