Assessment: Quadratic Functions

What does a negative value of a do to the graph of y = ax²?

If a quadratic's discriminant is 0, how many real roots does it have?

What is the vertex of y = x² + 6x + 5?

Solve x² + 2x − 8 = 0 for the larger root.

Find the discriminant of 3x² − 2x + 4 = 0.

Solve x² − 5x + 6 ≤ 0.

A ball's height is h(t) = −t² + 8t (t in seconds). At what time does it reach its maximum height?

A ball's height is h(t) = −5t² + 20t + 1. Why is the quadratic formula the best tool to find when it lands (h=0)?

A quadratic has vertex (2, −5) and passes through (0, 3). What is a? (Hint: use y = a(x−2)² − 5, then substitute (0,3).)

For what value of k does x² + 6x + k = 0 have exactly one repeated root?