Math 2-Unit 1 Midterm Review Day 1

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What is a linear function?

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A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a quadratic function?

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A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

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What does it mean for a function to be recursive?

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A recursive function is a function that calls itself in its definition, allowing it to solve problems by breaking them down into smaller, more manageable sub-problems.

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How do you find the roots of a polynomial equation?

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To find the roots of a polynomial equation, set the equation equal to zero and solve for the variable. This can involve factoring, using the quadratic formula, or other algebraic methods.

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What is the difference between linear and quadratic functions?

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Linear functions produce a straight line when graphed, while quadratic functions produce a parabola. Linear functions have a degree of 1, and quadratic functions have a degree of 2.

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What is the significance of the slope in a linear function?

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The slope (m) in a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

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What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

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What is the vertex of a parabola?

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The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula x = -b/(2a) for the vertex's x-coordinate.

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What is the difference between a linear and an exponential growth?

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Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals, leading to much faster growth over time.