What transformation would need to happen for the equation of the line to be y = 3/3 * x ^ 2
(1 point)
Shift the graph right 3, down 2
Shift the graph left 2
Shift the graph down 3, left 2
Shift the graph down 2
The transformation that would need to happen for the equation of the line to be y = 3/3 * x^2 is to shift the graph down 2.
4. Given the table for x, time in minutes, and y, distance traveled!
x: time
8
5
7
2
9
y: distance
664
415
581
166
747
(4 points)
a Every minute
meters are traveled
b. Write an equation to show the relationship between x and y
c. This relationship is
because the y-intercept is
a. The distance traveled is not consistent for every minute. It varies depending on the time.
b. In order to find an equation to show the relationship between x and y, we can use the method of least squares to find a line of best fit. Using a mathematical software or spreadsheet program, we can input the values of x and y and find the equation that best fits the data. However, without the full table of values, it is not possible to determine the equation.
c. Without knowing the equation or having more information, it is not possible to determine the relationship between x and y or the value of the y-intercept.
To transform the equation y = 3/3 * x^2 to the desired form, y = 3/3 * (x - h)^2 + k, where (h,k) represents the vertex of the parabola, the transformation needed is:
Shift the graph down 2
To transform the equation of a line from the standard form y = mx^2 to y = (3/3)x^2, you need to apply two transformations: a horizontal shift and a vertical shift.
Looking at the given equation, y = (3/3)x^2, we notice that the coefficient of x^2 is already 3/3, which simplifies to 1. This tells us that there is no need to stretch or compress the graph vertically.
However, we need to perform a horizontal and a vertical shift. The original equation y = x^2 has its vertex at the origin (0,0). To shift the graph horizontally, we have to either add or subtract a value from x. Similarly, to shift the graph vertically, we add or subtract a value from y.
Comparing the given equation y = (3/3)x^2 to the original equation y = x^2, we can see that the graph is shifted down. Therefore, we need to shift the graph down by a certain amount.
Since the original vertex is at (0,0) and the new vertex is at (0,-2), we can conclude that the transformation required is to shift the graph down by 2 units.
The correct answer is: Shift the graph down 2.