Find a model for the set of values.
x –5 –4 0 4 5
y 25 16
2
16 25(1 point)
Responses
graph a
Image with alt text: graph a
graph b
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graph c
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graph d
Image with alt text: graph a
To find a model for the set of values, we need to identify the pattern or relationship between the x and y values. Looking at the given values, we can observe that for x = -5, y = 25, and for x = -4, y = 16.
To find the relationship between x and y, let's examine the differences between consecutive y values:
Difference between y values: 25 - 16 = 9
Difference between x values: -5 - (-4) = -1
We can see that the y values are decreasing by 9 each time the x value increases by 1.
To find the general formula for this relationship, we can use the slope-intercept form of a linear equation:
y = mx + b
where:
m is the slope (rate of change)
b is the y-intercept (the value of y when x = 0)
Since the y values decrease by 9 each time the x value increases by 1, the slope is -9.
Substituting the values for x and y from the given data, we can solve for the y-intercept:
25 = -9(-5) + b
25 = 45 + b
b = -20
Therefore, the model for the set of values is:
y = -9x - 20
To find a model for the set of values, we need to analyze the relationship between the given x-values and y-values.
Looking at the values provided:
x: -5, -4, 0, 4, 5
y: 25, 16, 2, 16, 25
From this data, we can observe that the y-values are symmetrical around the x=0 line. This suggests that the data might be following a quadratic function.
Let's plot the points on a graph to visualize the relationship:
- x: -5 corresponds to y: 25
- x: -4 corresponds to y: 16
- x: 0 corresponds to y: 2
- x: 4 corresponds to y: 16
- x: 5 corresponds to y: 25
Now, let's plot these points on a graph:
- The x-axis represents x-values.
- The y-axis represents y-values.
Based on the plotted points, we can see that the points form a symmetrical curve. This suggests that the equation of the curve might be a parabolic function.
In this case, a possible model for the set of values is the equation of a parabola. The general form of a quadratic equation is:
y = ax^2 + bx + c
To find the specific coefficients a, b, and c for the equation, we can use any of the three provided points, since all the points lie on the same curve.
Let's choose the point (0, 2) to substitute into the equation:
2 = a(0)^2 + b(0) + c
2 = 0 + 0 + c
c = 2
Now we have the value of c.
Next, let's substitute the point (-4, 16) into the equation to find the value of a and b:
16 = a(-4)^2 + b(-4) + 2
16 = 16a - 4b + 2
14 = 16a - 4b
Finally, let's substitute the point (4, 16) into the equation to get another equation:
16 = a(4)^2 + b(4) + 2
16 = 16a + 4b + 2
14 = 16a + 4b
Now, we have a system of two equations:
14 = 16a - 4b
14 = 16a + 4b
By solving this system of equations, we can find the values of a and b, which will give us the complete model for the set of values.
Solving this system of equations, we find that a = 0.25 and b = 0.
Therefore, the model for the set of values is:
y = 0.25x^2 + 2.