Polynomial & Rational Function Word Problems Exam

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer and a_n ≠ 0.

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What is a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials. The general form is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) ≠ 0.

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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 polynomial equal to zero and solve for the variable. This can be done using factoring, the quadratic formula, or numerical methods.

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What is the axis of symmetry in a quadratic function?

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The axis of symmetry of a quadratic function in the form y = ax^2 + bx + c is given by the formula x = -b/(2a). It is a vertical line that divides the parabola into two mirror-image halves.

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How do you determine the vertex of a parabola?

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The vertex of a parabola represented by the equation y = ax^2 + bx + c can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

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

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The discriminant, given by D = b^2 - 4ac in the quadratic equation ax^2 + bx + c = 0, determines the nature of the roots. 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 solve a word problem involving the product of two numbers?

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To solve a word problem involving the product of two numbers, define the variables for the two numbers, set up an equation based on the product, and use any additional information (like their sum or difference) to create a system of equations.

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What is the formula for the height of a projectile?

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The height of a projectile can be modeled by the quadratic equation h(t) = -gt^2 + v_0t + h_0, where g is the acceleration due to gravity, v_0 is the initial velocity, and h_0 is the initial height.

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How do you set up an equation for a cost problem?

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To set up an equation for a cost problem, identify fixed costs and variable costs, then express the total cost as a function of the number of units or time, typically in the form y = mx + b, where m is the variable cost per unit and b is the fixed cost.

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What is the relationship between distance, rate, and time?

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The relationship between distance, rate, and time is given by the formula: Distance = Rate × Time. This can be rearranged to find any of the three variables if the other two are known.