Quadratic Functions Review

Which of the following is a quadratic function?

• f(x) = 2x + 1

• f(x) = 3x² - 2x + 1

• f(x) = 5x

• f(x) = 4x³ + 2x² - x

What are the different forms of representation of a quadratic function?

• Vertex, slope-intercept, and factored form

• Intercept, point-slope, and standard form

• Vertex, standard, and factored form

• Intercept, slope-intercept, and vertex form

Which form of a quadratic function is f(x) = a(x-h)² + k?

• Standard form

• Vertex form

• Factored form

• Intercept form

What is the role of the discriminant in quadratic equations? (multiple correct answers)

• It determines the number of x-intercepts of the quadratic function

• It determines the

  y-coordinate of the vertex of the parabola

• It determines the slope of the quadratic function

• It determines the nature of the roots of the quadratic equation

How does the parameter 'a' affect the graph of a quadratic function? (multiple correct answers)

• It controls the vertical stretch or compression of the parabola

• It determines the

  x-coordinate of the vertex

• It determines the number of x-intercepts of the parabola

• It determines whether

  the parabola opens upwards/downwards

Which of the following transformations affects the parameter 'k' in a quadratic function written in vertex form?

• Horizontal translation

• Vertical translation

• Vertical stretch or compression

• Reflection across the x-axis

What does the position of the parabola with respect to the x-axis indicate about the nature of the roots?

(multiple correct answers)

• If the parabola intersects the x-axis, the roots are real and distinct

• If the parabola does not intersect the x-axis, there are complex roots

• If the parabola is tangent to the x-axis, the roots are real and equal

• If the parabola opens upward, the roots are complex

Which of the following represents a quadratic equation with two real and equal roots? (multiple correct answers)

• x² - 4x + 4 = 0

• x² + 2x + 1 = 0

• x² + 3x + 2 = 0

• x² - 6x + 9 = 0

If the discriminant of a quadratic equation is negative, what can you conclude about the nature of its roots?

• The quadratic equation has two real and equal roots

• The quadratic equation has two real and distinct roots

• The quadratic equation has no real solutions

• The quadratic equation has one real and one imaginary root

What does the discriminant of a quadratic equation equal to zero indicate?

• The quadratic equation has two real and equal roots

• The quadratic equation has two real and distinct roots

• The quadratic equation has no real solutions

• The quadratic equation has one real and one imaginary root