Math 1 EOC: Exponential and Quadratic Functions

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What is depreciation in the context of exponential functions?

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Depreciation refers to the reduction in the value of an asset over time, often expressed as a percentage of the original value. In exponential functions, it can be modeled using the formula: V = P(1 - r)^t, where V is the value after time t, P is the initial value, r is the rate of depreciation, and t is time.

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How do you calculate the value of an asset after a certain number of years of depreciation?

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To calculate the value of an asset after depreciation, use the formula: V = P(1 - r)^t, where V is the future value, P is the initial value, r is the annual depreciation rate (as a decimal), and t is the number of years.

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What is a quadratic function?

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

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What are the zeros of a quadratic function?

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The zeros of a quadratic function are the values of x for which the function equals zero. They can be found by factoring, using the quadratic formula, or completing the square.

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How do you find the zeros of the quadratic equation x^2 + 2x - 15 = 0?

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To find the zeros, factor the equation: (x + 5)(x - 3) = 0. The zeros are x = -5 and x = 3.

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What is the vertex of a quadratic function?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula: x = -b/(2a) for the x-coordinate, and then substituting back to find the y-coordinate.

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What does the graph of a quadratic function look like?

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The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

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How do you determine the maximum or minimum value of a quadratic function?

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The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens upwards, the vertex represents the minimum value; if it opens downwards, it represents the maximum value.

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What is the significance of the discriminant in a quadratic equation?

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The discriminant (D = b^2 - 4ac) determines the nature of the roots of a quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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How do you express exponential growth mathematically?

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Exponential growth can be expressed with the formula: y = a(1 + r)^t, where a is the initial amount, r is the growth rate (as a decimal), and t is time.