抛物线图象与二次建模

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of 7 meters above the ground and reached a maximum height of 51.1 meters above the ground 3 seconds after the launch. How many seconds after the launch does the model estimate that the projectile will return to a height of 7 meters?

The table shows three values of x and their corresponding values of y , where y = f(x) +4 and f is a quadratic function. What is the y-coordinate of the y-intercept of the graph of y = f(x) in the xy-plane?

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. The model indicates the object has an initial height of 10 feet above the ground and reaches its maximum height of 1,034 feet above the ground 8 seconds after being launched. Based on the model, what is the height, in feet, of the object above the ground 10 seconds after being launched?

The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when t = 0, then what is the total distance traveled, in meters, by the object after 30.0 seconds?

h(x) =-16x² + 100x  +10

The quadratic function above models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If y = h(x)  is graphed in the xy-plane, which of the following represents the real-life meaning of the positive x-intercept of the graph?

A machine launches a softball from ground level. The softball reaches a maximum height of 51.84 meters above the ground at 1.8 seconds and hits the ground at 3.6 seconds. Which equation represents the height above ground h, in meters, of the softball t seconds after it is launched?

 f(x) =-500x² +25,000x

The revenue  f(x) , in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y = f(x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?

The y-intercept of the graph of \( y=x^2+31 \)  in the xy-plane is (0, y). What is the value of y?

The graph shows the height above ground, in meters, of a ball x seconds after the ball was launched upward from a platform. Which statement is the best interpretation of the marked point (1.0 , 4.8) in this context?

y =0.25x² -7.5x +90.25
The equation gives the estimated stock price y, in dollars, for a certain company x days after a new product launched, where 0≤ x ≤20. Which statement is the best interpretation of (x, y)=(1, 83)  in this context?

The parabola shown intersects the y-axis at the point (x, y). What is the value of y?

An object is kicked from a platform. The equation h =−4.9t² + 7t + 9 represents this situation, where h is the height of the object above the ground, in meters, t seconds after it is kicked. Which number represents the height, in meters, from which the object was kicked?