Understanding Quadratic Functions and Zeros

This video tutorial explains how to factor quadratic expressions where the leading coefficient is not one by using the graph of the related quadratic function. It covers determining the zeros of the function, which are the x-values that make the function value zero, and how these zeros relate to the factors of the quadratic expression. The video provides two examples: one involving a perfect square trinomial and another with distinct zeros, demonstrating the process of using a graphing calculator to find zeros and convert them into factored form.

What is the form of a quadratic expression that we are focusing on in this video?

• ax^2 + bx + c where b is 0

• ax^2 + bx + c where c is 0

• ax^2 + bx + c where a is not 1

• ax^2 + bx + c where a is 1

What do the zeros of a quadratic function represent in terms of factoring?

• The maximum points of the graph

• The minimum points of the graph

• The factors of the quadratic expression

• The slope of the tangent line

How many horizontal intercepts can a quadratic function have?

• Zero, one, or two

• Three

• Two

• One

What does it mean if a quadratic graph has one horizontal intercept?

• It has no binomial factors

• It has a double zero

• It has two distinct binomial factors

• It is a linear function

In the example y = 16x^2 + 24x + 9, what is the value of the double zero?

• 3/4

• 1/2

• -1/2

• -3/4

Why do we multiply the binomials by 4 in the first example?

• To change the sign of the factors

• To increase the degree of the polynomial

• To clear the fractions from the binomials

• To simplify the expression

What is the result of having two identical binomial factors in a quadratic expression?

• A linear expression

• A perfect square trinomial

• A constant expression

• A cubic expression

In the second example, what are the zeros of the quadratic y = 18x^2 + 21x - 4?

• 1/3 and -1/4

• -4/3 and 1/6

• 4/3 and -1/6

• -1/3 and 1/4

What is the purpose of converting decimals to fractions in the second example?

• To change the function's domain

• To find exact values for the zeros

• To simplify the calculation

• To make the graph look better

How do we clear fractions from the binomials in the second example?

• By multiplying by integers

• By multiplying by the reciprocal

• By adding a constant

• By dividing by integers