Quadratic Functions and Their Properties

Consider the function f(x) = (m² - 4)x² + 3x - 1. For this function to be classified as a quadratic function, what must be true about the value of 'm'?

• m must be equal to 2

• m must be equal to -2

• m must not be equal to 2 and m must not be equal to -2

• m can be any real number

In a quadratic function of the form y = ax² + bx + c, which coefficient determines the direction of the parabola's opening (concavity)?

• The coefficient 'b'

• The constant term 'c'

• The sign of the coefficient 'a'

• The discriminant (Δ)

What are the coordinates of the vertex for the quadratic function y = x^2 - 6x + 5?

• (3, 4)

• (-3, -4)

• (3, -4)

• (-3, 4)

A quadratic function has a discriminant (Δ) less than zero and its leading coefficient (a) is also less than zero. Which of the following statements accurately describes its graph?

• The parabola opens upwards and intersects the x-axis at two distinct points.

• The parabola opens downwards and touches the x-axis at exactly one point.

• The parabola opens upwards and does not intersect the x-axis.

• The parabola opens downwards and does not intersect the x-axis.

A projectile's height (H) in meters at time (t) in seconds is described by the function H(t) = -t^2 + 8t. What is the maximum height reached by the projectile?

• 4 meters

• 8 meters

• 16 meters

• 32 meters