1. The width that will maximize the area of the rectangle can be found by finding the x-coordinate of the vertex of the quadratic function. In this case, the vertex can be found at w = 8 meters. Therefore, the answer is A. 8 meters.
2. The horizontal length of the jump can be determined by finding the x-intercepts of the quadratic function. In this case, the x-intercepts can be found at d = -2 and d = 2. Therefore, the horizontal length of the jump is 4 meters. The maximum height can be found by finding the y-coordinate of the vertex of the quadratic function. In this case, the vertex can be found at (0, 1). Therefore, the maximum height is 1 meter. Therefore, the answer is D. The horizontal length of the jump is 4 meters and the maximum height is 1 meter.
3. By graphing the function f(x) = 1/2x^2 - 2x using technology, we can see that the vertex is at (2, -2) and the y-intercept is at (0, 0). Therefore, the statement "The vertex and the y-intercept of f(x) are at the same point" is false. Therefore, the answer is not A.
4. By graphing the function h(t) = -2t^2 + 6t - 4 using technology, we can see that the vertex is at (1.5, 0.5), the zeros are at (-1, 0) and (2, 0), and the y-intercept is at (0, -4). Therefore, the statement "The vertex of h(t) is at (3/2, 1/2)" is false. Therefore, the answer is not A.
1. The area of a rectangle A in square meters is modeled by the quadratic function A(w)=w(16−w), where w represents the width of the rectangle in meters. The graph of A(w) is given below. How long is the width so that the area of the rectangle is at its maximum?
A. 8 meters
B. 64 meters
C. 16 meters
D. 32 meters
2. . The path of an athlete's long jump is modeled by a function -1/4d^2+d
where d and h denote the distance and the height in meters respectively. The graph of h(d) is given by: Based on the function h(d), determine the horizontal length and the maximum height of this jump.
A. The horizontal length of the jump is 2 meters and the maximum height is 1/2 meter.
B. The horizontal length of the jump is 2 meters and the maximum height is 1 meter.
C. The horizontal length of the jump is 4 meters and the maximum height is 1/4 meter.
D. The horizontal length of the jump is 4 meters and the maximum height is 1 meter.
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
1 answer
1 answer