Algebra 2- Units 1 - 4 Review

Front

What is the range of a graph?

Back

The range of a graph is the set of all possible output values (y-values) that the function can produce. For example, if the range is 1 ≤ y ≤ 5, it means the function can output any value from 1 to 5, inclusive.

Front

Calculate (3 + 8i)(-2 - i).

Back

2 - 19i

Front

What form is the equation y=2x²-6x+1 in?

Back

Standard Form

Front

Find the vertex of the parabola given by the equation y = 3(x + 5)² - 4.

Back

(-5, -4)

Front

What is the result of (2 + 3i)²?

Back

-5 + 12i

Front

Define the vertex of a parabola.

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It can be found using the formula (-b/2a, f(-b/2a)) for a quadratic equation in standard form.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Explain what complex numbers are.

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, defined as √(-1).

Front

What is the discriminant of a quadratic equation and what does it indicate?

Back

The discriminant is given by the formula b² - 4ac. It indicates the nature of the roots of the quadratic equation: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x - h)² + k), you can complete the square.