1. Graphing Quadratic Equations
Objective: SWBAT graph quadratic equations

2. Parabolas Examples
The path of a jump shot as the ball travels toward the basket is a parabola.

3. Key terms
Parabola – a curve that can be modeled with a quadratic function.
Quadratic function – a function that can be written in the form

4. Key terms - continued
Vertex – the point where a parabola crosses its line of symmetry.
Maximum – the vertex of a parabola that opens downward. The y-coordinate of the vertex is the maximum value of the function.
Minimum – the vertex of a parabola that opens upward. The y-coordinate of the vertex is the minimum value of the function.
y-intercept – the y-coordinate of the point where a graph crosses the y-axis.
x-intercept – the x-coordinate of the point where a graph crosses the x-axis.
Line of symmetry

5. Lucky for you… …graphing parabolas won’t get that difficult.
For right now, we are sticking with parabola shifts.
given: y = (x – h)2 + k
h shifts the parabola a units to the right
-h shifts the parabolas a units to the left
k shifts the graph up b units
-k shifts the graph down b units
Integrated Graphing Quadratic Functions

6. Example 1

7. Direction and Min/Max
The graph of the quadratic function , is a parabola.
If a is positive
the graph opens up
the vertex is a minimum
If a is negative
the graph opens down
the vertex is a maximum
Note that the parabola does not have a constant slope. In fact, as x increases by 1 , starting with x = 0 , y increases by 1, 3, 5, 7,… . As x decreases by 1 , starting with x = 0 , y again increases by 1, 3, 5, 7,… .

8. Example 1

9. Example 1 - Answers

10. Graphing y = a(x - h)2 + k
In addition to shifting the parabola up, down, left, and right, we can stretch or shrink the parabola vertically by a constant. We can make a data table for the graph of y = 2x 2 :
Data Table for y = 2x 2
Here, the y increases from the vertex by 2, 6, 10, 14,… ; that is, by 2(1), 2(3), 2(5), 2(7),… .

11. In general, in the graph of y = a(x - h) + k , as x increases or decreases by units of 1 starting from the vertex, y increases by 1a, 3a, 5a, 7a,… .

12. Vertical Shrink or Stretch? Reflection over x-axis?
Summarize g(x) = ax2
Value of a
Vertical Shrink or Stretch?
Reflection over x-axis?
a > 1
0 < a < 1
-1 < a < 0
a = 1
a < -1

13. Example 2

14. Example 2 - Answers

15. Putting it all together…
y = a(x-h)2 + k