Question
If y = 3x2 + 6x + 2 is graphed in the xy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
- y-coordinate of the vertex
- x-intercept(s)
- y-intercept
- x-intercept of the line of symmetry
The correct answer is: y-intercept
○ The concept used in the question is understanding of equation.
○ The equation has a unique output for every input.
- Step by step explanation:
○ Given:
Graph of y = 3x2 + 6x + 2
○ Step 1:
Compare given equation with general equation of quadratic equation i.e
ax2 + bx + c.
We get,
a = 3, b = 6 and c = 2
So, 2 is constant term.
○ Step 2:
Put x = 0 in equation.
y = 3x2 + 6x + 2,
y = 3(0)2 + 6(0) + 2
y = 2
This is y-intercept.
- Final Answer:
Correct option.
Option C. y-intercept.
A linear equation is a two-variable equation with a line as the graph. A collection of points in the coordinate plane that are all solutions to the equation make up the graph of the linear equation. If every variable has a real value, the equation can be graphed by placing enough points on the graph to identify a pattern, then connecting those points to include all of the points.
Try to include zero as well as both positive and negative numbers when selecting your points. The two locations where the graph crosses the axes can be used if you want to utilize two points to draw your line. The x-intercept and y-intercept of a graph are the points where the axes cross, respectively. The value of x can be determined when y = 0 (x, 0) yields the x-intercept, and similarly, determining the value of y when x = 0 yields the y-intercept (0, y).
Related Questions to study
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?
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.
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?
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.
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.
