Algebra 2 Final Exam - Fall 24

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, a polynomial in standard form is expressed as: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

How do you simplify the square root of a negative number?

Back

To simplify the square root of a negative number, use the imaginary unit 'i', where i = √(-1). For example, √(-100) = √(100) * √(-1) = 10i.

Front

What is a minimum value in the context of a quadratic function?

Back

The minimum value of a quadratic function occurs at its vertex when the parabola opens upwards. It is the lowest point on the graph of the function.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots. Then, set each factor equal to zero and solve for x.

Front

What is the result of multiplying two complex numbers (5+i)(2+5i)?

Back

The result of multiplying (5+i)(2+5i) is 5*2 + 5*5i + 2i + 5i^2 = 10 + 25i + 2i - 5 = 5 + 27i.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 9x^3 + 8x^2 - 3x - 11, the degree is 3.

Front

What is the difference between a rational and an irrational number?

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A rational number can be expressed as a fraction of two integers (e.g., 1/2, 3, -4), while an irrational number cannot be expressed as a simple fraction (e.g., √2, π).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0. It is given by: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing on an interval if, as x increases, the function's value also increases. It is decreasing if, as x increases, the function's value decreases.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. For a quadratic function in standard form y = ax^2 + bx + c, the vertex can be found at x = -b/(2a).