10.2: Quadratic Functions
Objective- To graph quadratic functions of the type y = ax² + bx + c and quadratic inequalities.
* * Graph of the Quadratic Function * *
The graph of y = ax² + bx + c has the line x =
b
as it’s __________________.
2a
The x-coordinate of the vertex is found by x = ___________
Example 1: Graph each function.
a.) y = 3x² + 6x + 1
b.) f(x) = x² - 6x + 8
Example 2 Real World Problem Solving: Fireworks- Suppose a particular star is projected from an
aerial firework at a starting height of 610 ft with and initial upward velocity of 88 ft/s. How long will
it take for the start to reach it’s maximum height? How far above the ground will it be?
**Use the falling object function: h = -16t² + v 0 + h 0 ; where v 0 is initial velocity and h 0 is the initial
height.
Symbol vs. Style
≥;≤
>;<
Example 3: Graph the Quadratic Inequalities.
a.) y > -x² + 6x - 5
b.) y ≤ x² + 2x - 5