How is a linear-quadratic system different from a quadratic-quadratic system in terms of the number of solutions the system may have?
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Answer:
You should be familiar with how to graph three very important types of equations:
Linear equations in slope-intercept form: y=mx+b
Exponential equations of the form: y=a(b)x
Quadratic equations in standard form: y=ax2+bx+c
In real-world applications, the function that describes a physical situation is not always given. Finding the function is an important part of solving problems. For example, scientific data such as observations of planetary motion are often collected as a set of measurements
presented in a table. One job for a scientist is to figure out which function best fits the data.
Using Differences to Determine the Model
By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs
If the first difference is the same value, the model will be linear.
If the second difference is the same value, the model will be quadratic.
If the number of times the difference has been taken before finding repeated values exceeds five, the model may be exponential or some other special equation.
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