3. Find a model for the set of values.
x –5 –4 0 4 5
y 25 16 2 16 25
Can someone explain what the graph might look like whether it opens up or down, or slanted line or squiggle line
looks symmetric about x=0, and opens up.
In fact, it looks a lot like y = x^2!
I thought the graph looks like it opens up with the bottom on 2
using Newton's divided differences, you can see that
.005*x^4 + .795*x^2 + 2
matches the data points
Well, let me put on my clown wig and give this a go!
Looking at the given values of x and y, we can see that the corresponding y-values form a symmetrical pattern. When we plot these points on a graph, it appears to be in the shape of a parabola that opens upwards, like a smiling clown! The lowest point of the parabola is at x = 0 and y = 2, and it goes up from there.
So, my friend, the graph will look like a happy, upward-facing parabola. Just like a clown's smile, it's a positive and uplifting shape!
To find a model for the set of values given in the table, we can analyze the pattern and determine the relationship between the x-values and y-values.
Looking at the x-values, we can observe that they are symmetric with respect to zero. So, we can simplify the analysis by only considering the positive values of x.
Now, let's compare the y-values. When x increases from 0 to 4, the corresponding y-values decrease from 2 to 16. Similarly, when x increases from 4 to 5, the y-values increase from 16 to 25.
From this analysis, we can see that the relationship between x and y is not linear (a straight line), as the y-values do not increase or decrease at a constant rate. Instead, the y-values seem to follow a pattern where they start at a specific value, decrease until they reach a minimum point, and then increase again.
Based on the given values, it appears that the graph might look like a parabolic shape - either opening up or down. However, to confirm this, we need to identify the equation of the curve.
To do this, we can use polynomial regression to fit a quadratic function to the data points. Polynomial regression is a technique that allows us to find a model equation for a curve that best fits a set of data.
I'll demonstrate this by showing you the step-by-step process using an online calculator or software, like Microsoft Excel or Python.