Semester Exam Review

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it in the form of (ax + b)(cx + d) such that the product equals the original expression. This is often done by finding two numbers that multiply to ac and add to b.

Front

What is the square root of 80 simplified?

Back

The square root of 80 can be simplified to 4√5.

Front

What is a quadratic model?

Back

A quadratic model is a mathematical representation of a relationship between variables that can be expressed in the form of a quadratic equation, typically written as y = ax^2 + bx + c.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when a quantity decreases at a rate proportional to its current value.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

The simplified expression is 11a^3 - 4a^2 - 14a - 7.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a function to be quadratic?

Back

A function is quadratic if it can be represented by a polynomial of degree 2, which means its highest exponent is 2.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, which determines the nature of the roots of the equation.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient of x^2 (a) is positive and downwards if it is negative.