Algebra 2: Mid Year Assessment

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you simplify the expression (2 + 4i)(3 + 5i)?

Back

To simplify, use the distributive property: (2)(3) + (2)(5i) + (4i)(3) + (4i)(5i) = 6 + 10i + 12i + 20i². Since i² = -1, this becomes 6 + 22i - 20 = -14 + 22i.

Front

What is the process to solve the equation 2x² - 5x = 1?

Back

First, rearrange the equation to standard form: 2x² - 5x - 1 = 0. Then apply the quadratic formula: x = (5 ± √(25 + 8)) / 4.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a ≠ 0.

Front

What is the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in the form y = ax² + bx + c is given by the line x = -b/(2a).

Front

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

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

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 √(-1).

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately: (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.