Factoring Quadratic Equations and Roots

The video tutorial covers writing quadratic equations in factored form, exploring the relationship between the roots and factors of a quadratic equation. It demonstrates graphing quadratic equations using a calculator and explains the zero product property. The tutorial provides detailed steps to write quadratic equations from given roots and convert them to standard form. Several example problems are solved to illustrate these concepts.

What is the factored form of the quadratic equation y = (x + 3)(x - 1)?

• x^2 + 4x - 3

• x^2 - 2x + 3

• x^2 + 2x - 3

• x^2 - 4x + 3

How are the roots of a quadratic equation related to its factors?

• They are different numbers with opposite signs.

• They are different numbers with the same signs.

• They are the same numbers with opposite signs.

• They are the same numbers with the same signs.

What is the first step in writing a quadratic equation in factored form?

• Identify the axis of symmetry.

• Identify the y-intercept.

• Identify the vertex.

• Identify the roots or solutions.

In the equation y = a(x - m)(x - n), what do m and n represent?

• The y-intercepts

• The x-intercepts or roots

• The coefficients of x

• The vertex coordinates

What is the standard form of the equation y = 3(x + 5)(x + 3)?

• 3x^2 + 15x + 45

• 3x^2 + 24x + 45

• 3x^2 + 8x + 15

• 3x^2 + 18x + 30

Which method can be used to multiply binomials in the conversion to standard form?

• Substitution method

• Graphing method

• FOIL method

• Elimination method

What is the value of 'a' if the equation is y = a(x + 3)(x - 1) and passes through the point (-5, -3)?

• 1/2

• -1/2

• 1/4

• -1/4

In the example using a table of values, what are the roots of the equation?

• -2 and 3

• 2 and -3

• -3 and 2

• 3 and -2

What is the factored form of the equation derived from the graph with roots at -1 and 4?

• y = (x - 1)(x + 4)

• y = (x + 1)(x + 4)

• y = -(x + 1)(x - 4)

• y = -(x - 1)(x + 4)

What is the standard form of the equation y = -(x + 1)(x - 4)?

• -x^2 + 3x + 4

• x^2 - 3x - 4

• -x^2 - 3x + 4

• x^2 + 3x - 4