Quadratic Functions Mrs Book Liberty Hill Middle School

Quadratic Functions Mrs. Book Liberty Hill Middle School Algebra I

Graph of a Quadratic Function The graph of y = ax 2 + bx + c, where a ≠ 0, has the line as its axis of symmetry. The x-coordinate of the vertex is

2 Graphing y = ax + bx + c Graph the function y = -3 x 2 + 6 x + 5. Step 1: Find the equation of the axis of symmetry and the coordinates of the vertex. The axis of symmetry is x = 1 y = -3 x 2 + 6 x + 5 y = -3(1)2 + 6(1) + 5 y = 8; The vertex is (1, 8)

2 Graphing y = ax + bx + c Step 2: Find two other points on the graph Use the y-intercept; x = 0 y = -3(0)2 + 6(0) + 5 y = 5; one point is (0, 5) Choose a value for x on the same side of the vertex as the y-intercept x = -1 y = -3(-1)2 + 6(-1) + 5 y = -4; one point is (-1, -4) Reflect (0, 5) and (-1, -4) across the axis of symmetry to get two more points. The draw the parabola.

2 Graphing y = ax + bx + c

2 Graphing y = ax + bx + c Graph f(x) = x 2 – 6 x + 9. Label the axis of symmetry and the vertex.

Real-World Problem Solving In professional fireworks displays, aerial fireworks carry “stars” upward, ignite them, and project them into the air. Suppose a particular star is projected from an aerial firework at a starting height of 520 ft. with an intial upward velocity of 72 ft/s. How long will it take for the star to reach its maximum height? How far above the ground will it be? The equation h = -16 t 2 + 72 t + 520 gives the star’s height h in feet at time t in seconds.

Real-World Problem Solving The equation h = -16 t 2 + 72 t + 520 gives the star’s height h in feet at time t in seconds. Since the coefficient of t 2 is negative, the curve opens downward, and the vertex is the maximum point. Step 1: Find the t-coordinate of the vertex After 2. 25 seconds, the star will be at its greatest height. Step 2: Find the h-coordinate of the vertex The maximum height of the star will be 601 ft.

Real-World Problem Solving A ball is thrown into the air with an initial upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function h = -16 t 2 + 48 t + 4. In how many seconds will the ball reach its maximum height? What is the ball’s maximum height?

Graphing Quadratic Inequalities Graph the quadratic inequality y ≤ x 2 – 3 x – 4.

Graph the Quadratic Inequalities y ≤ x 2 + 2 x – 5 y > x 2 + x + 1