Final Exam Study Guide

Front

How many radians does a circle have?

Back

A circle has 2π radians.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

Factor x² + 6x + 9.

Back

(x + 3)(x + 3); x = -3.

Front

What is the result of factoring by grouping for x³ - 4x² - 4x + 16?

Back

(x - 4)(x - 2)(x + 2).

Front

Identify the quadratic function represented by the graph: y = -2(x + 4)² + 5.

Back

This function opens downwards and has a vertex at (-4, 5).

Front

What is the formula for converting degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots.

Front

How do you determine if a trinomial is a perfect square?

Back

Check if it can be expressed as (a ± b)², meaning the first and last terms are perfect squares and the middle term is twice the product of the square roots.

Front

What is the factored form of x² - 9?

Back

(x - 3)(x + 3).