1. ALGEBRA 2 Section 5.2: Properties of Quadratic Functions in Standard Form

2. Symmetry
Axis of Symmetry = line that when you flip the parabola over it, it lands on itself
f(x) = x2
Axis is the y-axis or x=0 line
Goes thru the vertex (0,0)
Vertical line
f(x) = a(x – h)2 + k
Axis is the vertical line _________
The axis gets shifted h units horizontally

3. Example 1: Identify the axis of symmetry.
A) y = 4(x – 3) B) f(x) = -1/2(x + 5)2 – 8

4. What happens when we expand Vertex Form to look like Standard Form
y = a(x – h)2 + k

5. a = a

6. b =–2ah

7. c = ah2 + k

8. Standard Form y = ax2 + bx + c
Questions that we can answer from Standard Form
Which way does the parabola open?
What is the axis of symmetry?
What is the vertex?
What is the y-intercept?

9. Example 2: f(x) = 2x2 – 4x + 5 Does it open up or down?
Find the axis of symmetry.
Find the vertex.
What is the y-intercept?
Graph the function

10. Example 3: f(x) = -x2 – 2x + 3 Does it open up or down?
Find the axis of symmetry.
Find the vertex.
What is the y-intercept?
Graph the function

11. Minimum & Maximum Values
Minimum = y-value of the vertex when parabola opens up
Domain:
Range:
Maximum = y-value of the vertex when parabola opens down
Domain:
Range:

12. Example 4:
Find the minimum or maximum value of f(x)=-3x2 + 2x – 4. Then state the domain and range of the function.

13. Example 5:
The average height h in centimeters of a certain type of grain can be modeled by the function h(r) = 0.024r2 – 1.28r , where r is the distance in centimeters between the rows in which the grain is planted. Based on this model, what is the minimum average height of the grain, and what is the row spacing that results in this height?

14. Assignment #2: Page 328 #’s 12-30,(56)