Polynomials Functions Recovery Test

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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: $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ where $$a_n, a_{n-1}, ..., a_0$$ are constants and $$n$$ is a non-negative integer.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in the polynomial $$2x^3 + 3x^2 - x + 5$$, the degree is 3.

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What is the conjugate of a complex number?

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The conjugate of a complex number $$a + bi$$ is $$a - bi$$. For example, the conjugate of $$3 + 2i$$ is $$3 - 2i$$.

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How do you multiply two complex numbers?

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To multiply two complex numbers, use the distributive property (FOIL method). For example, to multiply $$(1 - 3i)(2 + 5i)$$, calculate: $$1*2 + 1*5i - 3i*2 - 3i*5i = 2 + 5i - 6i - 15 = 17 - i$$.

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What does it mean for a function to be increasing?

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A function is increasing on an interval if, for any two points $$x_1$$ and $$x_2$$ in that interval, if $$x_1 < x_2$$ then $$f(x_1) < f(x_2)$$.

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What does it mean for a function to be decreasing?

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A function is decreasing on an interval if, for any two points $$x_1$$ and $$x_2$$ in that interval, if $$x_1 < x_2$$ then $$f(x_1) > f(x_2)$$.

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What is the standard form of a quadratic function?

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The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ where $$a, b, c$$ are constants and $$a eq 0$$.

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What is the vertex of a parabola?

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The vertex of a parabola represented by the quadratic function $$f(x) = ax^2 + bx + c$$ can be found using the formula: $$x = -\frac{b}{2a}$$. The corresponding $$y$$ value can be found by substituting $$x$$ back into the function.

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What is the discriminant of a quadratic equation?

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The discriminant of a quadratic equation $$ax^2 + bx + c = 0$$ is given by $$D = b^2 - 4ac$$. It 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 two complex roots.

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How do you simplify the expression $$\sqrt{-1}$$?

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The expression $$\sqrt{-1}$$ is defined as the imaginary unit $$i$$. Therefore, $$\sqrt{-1} = i$$.