Final Exam Review

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What is a quadratic model?

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A quadratic model is a mathematical representation of a relationship between variables that can be expressed in the form of a quadratic equation, typically written as y = ax² + bx + c, where a, b, and c are constants.

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How do you identify the best fitting quadratic model for a set of data?

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To identify the best fitting quadratic model, you can use methods such as least squares regression, which minimizes the sum of the squares of the differences between observed and predicted values.

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What is a linear equation?

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A linear equation is an equation that describes a straight line when graphed on a coordinate plane, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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What does the slope of a linear equation represent?

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The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

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What is the y-intercept in a linear equation?

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The y-intercept is the value of y when x is equal to zero. It is the point where the line crosses the y-axis.

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How do you write the equation of a line given two points?

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To write the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to find the equation.

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What is the domain of a relation?

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The domain of a relation is the set of all possible x-values (input values) for which the relation is defined.

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What is the range of a relation?

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The range of a relation is the set of all possible y-values (output values) that result from the domain.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

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How do you determine if a relation is a function?

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To determine if a relation is a function, use the vertical line test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.