Determining Rational X Intercepts of Quadratic Functions through Factoring

This video tutorial explains how to determine the number of rational X intercepts in the graph of a quadratic function by examining the factorization method used. It covers the concept of rational and irrational numbers, the zero product property, and different types of quadratic functions, including factorable functions, monomial factorization, perfect square trinomials, and trinomials with different factors. The tutorial emphasizes that factorable functions have rational X intercepts, while non-factorable ones may have irrational intercepts. It also highlights the significance of the graph's symmetry and the role of the Y-axis.

What is a common misunderstanding about non-factorable functions?

• They always have irrational X intercepts.

• They have no X intercepts.

• They have only one X intercept.

• They have infinite X intercepts.

How can you determine the number of rational X intercepts for the function F(x) = x^2 - 4?

• By using the quadratic formula.

• By factoring it as a difference of squares.

• By completing the square.

• By graphing the function.

What is the significance of the X intercept being zero in a quadratic function?

• The parabola has no symmetry.

• The parabola has a vertical asymptote.

• The parabola passes through the origin.

• The parabola is tangent to the X axis.

What does it mean if a quadratic trinomial has identical solutions?

• The graph has infinite X intercepts.

• The graph has two distinct X intercepts.

• The graph has one X intercept.

• The graph has no X intercepts.

How can you tell if a quadratic trinomial will have two different X intercepts?

• If the trinomial is not factorable.

• If the trinomial is a perfect square.

• If the trinomial has a zero constant term.

• If the factors of the trinomial are different.