Algebra 2 TN EOC Review Assignment (Fall 2024)

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What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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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 the direction it opens. For the function f(x) = ax² + bx + c, the vertex can be found at the point (h, k) where h = -b/(2a) and k = f(h).

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What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by D = b² - 4ac. It indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are no real roots.

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How do you solve a quadratic equation by factoring?

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To solve a quadratic equation by factoring, express the equation in the form ax² + bx + c = 0, factor it into the form (px + q)(rx + s) = 0, and then set each factor equal to zero to find the solutions.

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What is the quadratic formula?

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The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

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What is a function's domain?

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

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What is a function's range?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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What is the difference between a linear function and a quadratic function?

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A linear function has a constant rate of change and is represented by a straight line (y = mx + b), while a quadratic function has a variable rate of change and is represented by a parabola (y = ax² + bx + c).

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values that satisfy all equations simultaneously.

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How do you graph a quadratic function?

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To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a smooth curve through them to form a parabola.