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Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Tags

CCSS.HSN.CN.A.1

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Tags

CCSS.HSN.CN.A.2

Front

What is the vertex of a quadratic function in vertex form?

Back

The vertex of a quadratic function in the form f(x) = a(x - h)^2 + k is the point (h, k).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept of a function, set x = 0 and solve for y.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function in standard form y = ax^2 + bx + c is given by the line x = -b/(2a).

Front

What is the difference between standard form and vertex form of a quadratic function?

Back

Standard form is y = ax^2 + bx + c, while vertex form is y = a(x - h)^2 + k. Vertex form makes it easier to identify the vertex (h, k).