Question
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?
- The initial height of the projectile
- The maximum height of the projectile
- The time at which the projectile reaches its maximum height
- The time at which the projectile hits the ground.
The correct answer is: The time at which the projectile hits the ground.
○ Concept used in the question is concept of graph of the quadratic equation.
○ Quadratic equation has two solutions.
○ Points at which graph cut x-axis are the solution of quadratic equation.
- Step by step explanation:
○ Given:
Graph of y = h(x) , of projectile motion.
○ Step 1:
We know that x-intercept will be of form (x,h) = (a,0)
Where h represent height and x represent time.
∴ at x = a,
h = o
Which means time a after it launched the height is zero which means it hits ground.
∴ x-intercept time at which projectile hits ground.
.
- Final Answer:
Correct option.
Option D. The time at which the projectile hits the ground.
Quadratic equations typically have two solutions because the solutions are where the parabola intersects the x-axis. The graph will cross twice if the vertex is below the x-axis and the parabola opens up, and twice if the vertex is above the x-axis and the parabola opens down.
Quadratic equation graphing to create a parabola graph, we must first determine the vertex of the given equation. This is possible by using x = -b/2a and y = f(-b/2a). The graph is plotted when the quadratic equation is given in the form f(x) = a(x-h)2 + k, where (h, k) is the vertex of the parabola.
Related Questions to study
Near the end of a US cable news show, the host invited viewers to respond to a poll on the show’s website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 28% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?
Those who responded to the pool were not a random sample of the population of the United States. Moreover, because the people were watching a US cable news show, it could not have been very objective. Thus the majority of those watching it shared the same political bias. Therefore, the program's viewers might need to accurately represent the entire American populace.
Getting highly responsive is not something that has any percentage of yes or no responses because what we're trying to find out is how people feel about it. So having 50-50 people is not a condition that the show needed to allow more time to respond to the information. So we need to know the time taken to respond to the pool and what percentage of people were at a discount.
Near the end of a US cable news show, the host invited viewers to respond to a poll on the show’s website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 28% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?
Those who responded to the pool were not a random sample of the population of the United States. Moreover, because the people were watching a US cable news show, it could not have been very objective. Thus the majority of those watching it shared the same political bias. Therefore, the program's viewers might need to accurately represent the entire American populace.
Getting highly responsive is not something that has any percentage of yes or no responses because what we're trying to find out is how people feel about it. So having 50-50 people is not a condition that the show needed to allow more time to respond to the information. So we need to know the time taken to respond to the pool and what percentage of people were at a discount.
The given equations are two different models that can be used to find the value, in dollars, of a particular car t years after it was purchased. Which of the following statements correctly compares the values of E and V for 0 < t < 9 ?
The given equations are two different models that can be used to find the value, in dollars, of a particular car t years after it was purchased. Which of the following statements correctly compares the values of E and V for 0 < t < 9 ?
The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?
The standard deviation is the degree of scatter or dispersion of the data points to their mean in descriptive statistics.
It provides information on the distribution of values within the data sample and verifies how widely apart the data points are from the mean.
A square root of the variance of a sample, statistical population, random variable, data collection, or probability distribution represents its standard deviation.
How to Calculate Standard Deviation
1.) Discover the observations' mean and arithmetic mean.
2.) Find the squared deviations from the mean. (The data value - mean) 2
3.) Calculate the squared difference average. (Variance = The total squared differences divided by the total number of observations)
4.) Determine the variance's square root. (Standard deviation = Square root of variance)
The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?
The standard deviation is the degree of scatter or dispersion of the data points to their mean in descriptive statistics.
It provides information on the distribution of values within the data sample and verifies how widely apart the data points are from the mean.
A square root of the variance of a sample, statistical population, random variable, data collection, or probability distribution represents its standard deviation.
How to Calculate Standard Deviation
1.) Discover the observations' mean and arithmetic mean.
2.) Find the squared deviations from the mean. (The data value - mean) 2
3.) Calculate the squared difference average. (Variance = The total squared differences divided by the total number of observations)
4.) Determine the variance's square root. (Standard deviation = Square root of variance)
The graph of the exponential function h in the xy-plane, where y = h(x), has a y-intercept of d, where d is a positive constant. Which of the following could define the function h ?
An exponential function is a mathematical function with the equation f (x) = an x. where x is a variable and an is a function's base constant. The most typical exponential-function base is the transcendental number e, or approximately 2.71828.
¶The formula for exponential functions is f(x) = bx, where b > 0 and b 1. As with any exponential expression, b and x are referred to as the base and exponent, respectively. Bacterial growth is an illustration of an exponential function. Some bacterial species reproduce hourly.
The graph of the exponential function h in the xy-plane, where y = h(x), has a y-intercept of d, where d is a positive constant. Which of the following could define the function h ?
An exponential function is a mathematical function with the equation f (x) = an x. where x is a variable and an is a function's base constant. The most typical exponential-function base is the transcendental number e, or approximately 2.71828.
¶The formula for exponential functions is f(x) = bx, where b > 0 and b 1. As with any exponential expression, b and x are referred to as the base and exponent, respectively. Bacterial growth is an illustration of an exponential function. Some bacterial species reproduce hourly.
