1. Exploring Quadratic Graphs
Students need graphing calculators and dry erase boards.
Mrs. Book
Liberty Hill Middle School
Algebra I

2. Bellwork Evaluate the expressions for h = 3, k = 2, and j = - 4 hkj
kh2
hk2
kj2 + h
1. -24; 2. 18; 3. 12; 4. 35

3. Graph each equation y = 2x – 1 y = |x| + 1 y = x2 + 2
Graph on graphing calculators

4. Quadratic Function
A quadratic function is a function that can be written in the form y = ax2 + bx + c.
This is the standard form of a quadratic function.

5. Parent Function
The simplest quadratic function, f(x) = x2 or y = x2, is the quadratic parent function.
Graph y = x2
The graph of a quadratic function is a U-shaped curve called a parabola.

6. Vocabulary
The axis of symmetry is the line that divides the parabola into two matching halves.
The vertex is the highest or lowest point of a parabola.

7. Vocabulary
The vertex is the minimum point, if a > 0 in y = ax2 + bx + c. This parabola opens upward.
The vertex is the maximum point, if a < 0 in y = ax2 + bx + c. This parabola opens downward.

8. Identify the vertex
Identify the coordinates of the vertex. Tell whether it is a minimum or maximum.

9. Identify the vertex
Identify the coordinates of the vertex. Tell whether it is a minimum or maximum.

10. Graphing y = ax2
Make a table of values and graph the quadratic function y = ½x2 x
y = ½x2
(x, y) 2 4
Students work out information on dry erase boards

11. Graphing y = ax2
Make a table of values and graph the quadratic function y = -2x2 x
y = -2x2
(x, y) 2 4
Students work out problems on dry erase boards

12. Comparing Widths of Parabolas
Order the quadratic functions f(x) = -4x2, f(x) = ¼x2, and f(x) = x2 from widest to narrowest graph.
Functions f(x) = ¼x2, f(x) = x2 , then f(x) = -4x2

13. Comparing Widths of Parabolas
Order the quadratic functions y = x2, y = ½x2, and f(x) = -2x2 from widest to narrowest graph.
Functions f(x) = ½x2, f(x) = x2 , then f(x) = -2x2

14. Comparing Widths of Parabolas
When |m| < |n|, the graph of y = mx2 is wider than the graph of y = nx2.
Functions f(x) = ½x2, f(x) = x2 , then f(x) = -2x2

15. Graphing y = ax2 + c
How is the graph of y = 2x2 + 3 different from the graph of y = 2x2 ? x
y = 2x2
y = 2x2 + 3 -2 -1 1 2
Have students make an educated guess on what will happen to the graph. Will it shift up, down, left, or right?
The graph of y = 2x2 + 3 has the same shape as the graph of y = 2x2 but it is shifted up 3 units.

16. Real-World Problem Solving
Suppose you see an eagle flying over a canyon. The eagle is 30 ft. above the level of the canyon’s edge when it drops a stick from its claws. The force of gravity causes the stick to fall toward Earth. The function h = -16t gives the height of the stick h in feet after t seconds. Graph this quadratic function.