Exploring Roots in Quadratic Equations

What does a zero of a function represent?

• The x-value where the function crosses the y-axis

• The maximum point of the function

• The x-value where the function crosses the x-axis

• The minimum point of the function

Which expression is a factor of a quadratic with zeros at x = -4 and x = 2?

• x + 4

• x - 4

• x - 2

• x + 2

What is the first step in factoring a quadratic equation?

• Find the difference of squares

• Identify the greatest common factor (GCF)

• Apply the quadratic formula

• Draw a sketch of the curve

What are the zeros of the function f(x) = 4x^2 - 100?

• x = 0

• x = 25 and x = -25

• x = 10 and x = -10

• x = 5 and x = -5

What does the GCF stand for in polynomial factoring?

• Greatest Common Factor

• Geometric Coefficient Function

• General Cubic Formula

• Graphical Curve Fitting

What is the result of factoring the expression x^2 - 25?

• (x - 5)^2

• x(x - 25)

• (x + 25)(x - 25)

• (x + 5)(x - 5)

What is the significance of the difference of perfect squares in factoring?

• It simplifies the expression to a single term

• It allows for the expression to be factored into linear terms

• It indicates the function has no real zeros

• It is used to find the vertex of the function

What method is used to factor a trinomial?

• Graphing

• Difference of squares

• Quadratic formula

• Product-sum method

How do you find the zeros of a cubic function?

• Plotting the function on a graph

• Setting the function equal to zero and factoring

• Finding the vertex of the cubic function

• Using the quadratic formula directly

Which of the following is a zero of the function f(x) = 2x^3 - 4x^2 - 6x?

• x = -1

• x = 1

• x = 2

• x = 0