Which of the following functions represents a parabola that has a vertex located at (–3,4), and that passes through the point (–1, –4)?

The graph of f(x) is shown above. If f(x) = _ax_2 + bx + c, where a, b, and c are real numbers, then which of the following must be true:

I. a < 0

II. c < 0

III. b_2 – 4_ac < 0

Let f(x) = ax2 + bx + c, where a, b, and c are all nonzero constants. If f(x) has a vertex located below the x-axis and a focus below the vertex, which of the following must be true?

I. a < 0

II. b < 0

III. c < 0

What is the vertex of the function ?

Best friends John and Elliot are throwing javelins. The height of John’s javelin is described as f(x) = -x2 +4x, and the height of Elliot’s javelin is described as f(x) = -2x2 +6x, where x is the horizontal distance from the origin of the thrown javelin. Whose javelin goes higher?

Where does the following equation intercept the x-axis?

Let f(x) = x2. By how many units must f(x) be shifted downward so that the distance between its x-intercepts becomes 8?

Where does the following equation intercept the -axis?

Where does the following equation intercept the -axis?