1. Properties of Quadratic Functions in Standard Form 5-1
SWBAT
Define, identify, and graph quadratic functions.
Identify and use maximums and minimums of quadratic functions to solve problems.
Holt Algebra 2

2. Vocabulary Quadratic Function: An equation with a degree of 2.
Standard Form:
y = ax2 + bx + c
Parabola:
A quadratic graph that has a U shape
Vertex:
The lowest or highest point of the graph
Axis of Symmetry:
The line passing through the vertex that divides the parabola in half

4. This shows that parabolas are symmetric curves
This shows that parabolas are symmetric curves. The axis of symmetry is the line through the vertex of a parabola that divides the parabola into two congruent halves.

5. These properties can be generalized to help you graph quadratic functions.

7. A is positive A is negative

8. Graphing a Quadratic Function
Step 1: Find the x-coordinate of the vertex
Step 2: Make a table.
Use 2 values to the left & right of the vertex
Step 3: Plot the points and make a curve similar to a U
Step 4: Analyze parts of the graph.

9. The minimum (or maximum) value is the y-value at the vertex
The minimum (or maximum) value is the y-value at the vertex. It is not the ordered pair that represents the vertex.
Caution!

10. Graph: f(x) = x2 – 4x + 4 x Work y
Standard Form: ___________ a =___ b =___ c = ___ Vertex: _____ D: _______ AOS: _____ R: _______ Min: _____ Max: _____ Zeros: _____ x
Work y

11. Graph: f(x) = x2 + 3x – 5 x Work y
Standard Form: ___________ a =___ b =___ c = ___ Vertex: _____ D: ________ AOS: _____ R: ________ Min: _____ Max: _____ Zeros: ____ x
Work y

12. Homework:
Pg 241 #14, 18, 22 – 30 even
Pg 249 #14 – 19 all

13. Properties of Quadratic Functions in Standard Form 5-1
SWBAT
Define, identify, and graph quadratic functions.
Identify and use maximums and minimums of quadratic functions to solve problems.
Holt Algebra 2

14. Solve for ‘t’ to find the zeros.

15. Without a graphing Calculator
Without a graphing Calculator. Find the vertex using your formula from yesterday.
If your lead coefficient is positive, it is a min, if it is negative, it is a max.

18. Think-Pair-Share: Review of Yesterday
Consider the function f(x)= 2x2 + 8x – 7.
1. Determine whether the graph opens upward or downward.
2. Find the axis of symmetry.
3. Find the vertex.
4. Identify the maximum or minimum value of the function.
5. Find the y-intercept.
6. Graph the function.
7. Find the domain and Range of the function.

19. Homework:
Pg 241 #51-54, 64