1. Mrs. Book Liberty Hill Middle School Algebra I
2/22/ :04 PM
Quadratic Functions
Mrs. Book
Liberty Hill Middle School
Algebra I
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2. Graph of a Quadratic Function
The graph of y = ax2 + bx + c, where a
≠ 0, has the line as its axis of
symmetry.
The x-coordinate of the vertex is

3. Graphing y = ax2 + bx + c Graph the function y = -3x2 + 6x + 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 = -3x2 + 6x + 5
y = -3(1)2 + 6(1) + 5
y = 8; The vertex is (1, 8)

4. Graphing y = ax2 + 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.

5. Graphing y = ax2 + bx + c

6. Graphing y = ax2 + bx + c
Graph f(x) = x2 – 6x Label the axis of symmetry and the vertex.

7. 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 = -16t2 + 72t gives the star’s height h in feet at time t in seconds.

8. Real-World Problem Solving
The equation h = -16t2 + 72t gives the star’s height h in feet at time t in seconds.
Since the coefficient of t2 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.

9. 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 = -16t2 + 48t + 4.
In how many seconds will the ball reach its maximum height?
What is the ball’s maximum height?

10. Graphing Quadratic Inequalities
Graph the quadratic inequality y ≤ x2 – 3x – 4.
Students use graphing calculators to graph the quadratic inequality

11. Graph the Quadratic Inequalities
y ≤ x2 + 2x – 5
y > x2 + x + 1