1. Warm-Up Find the x and y intercepts: 1. f(x) = (x-4)2-1
2. f(x) = -2(x-3)(x+4)
3. f(x) = x2-2x -15
Homework: 3.1 A Worksheet due 10/18
3.1B Worksheet due 10/19

2. Lesson 3.1 Quadratic Functions– The Three Forms
1. Standard or General Form
y = ax2+ bx + c
This form tells me the __________________.
That is where the graph ________________.
The y-intercept is _____________________.
y-intercept
crosses the y-axis
(0,c)

3. 2. Factored Form y = a( x – r1) (x-r2)
This form tells me the __________________.
That is where the graph ________________.
To find the roots, zeros or x-intercepts _______________.
roots, zeros, or x-intercepts
crosses the x-axis
Set ( x – r1) (x-r2) = 0

4. 3. Vertex Form y = a( x –h)2+k
This form tells me the __________________.
That is where the graph ________________.
The vertex is _____________________.
vertex
Minimum or maximum of the parabola
(h,k)

5. How to convert from different forms? Given:

6. Given:

7. Given:

8. Ex. 1: y = x2-6x + 5 General Form What form?
Change from general to ____________ by using either _______________ or ___________________.
Factored Form
Factoring
Quadratic Formula
X2 – 6x + 5
(x-5)(x-1) = 0
X = 5, x = 1

9. Ex. 2: y = x2-6x + 5 y = x2-6x + 5 Complete the square
Change from general form to __________ by using _________________________.
Vertex form
Completing the square
y = x2-6x + 5 Complete the square
(x2-6x + _____) = _____ 9 9
(x-3)2 -4 = y
Now Graph:
Y-intercept:_______
Vertex :_______
X-intercepts: ______, ______
(0,5)
(3,-4)
(5,0) (1,0)

10. Ex. 3: Using f(x) = -3x2 +6x - 13 find the vertex when given the standard form?
Use the formula to find x :
Substitute in x to find y.
In standard form a = -3, b = 6, c= -13
x = 1 , then y = -3(1)2 +6(1) -13 = -10
Vertex = (1, -10)

11. 3b. You try: y = (x+4)2-13
HINT: If you cannot factor it, you must use the Quadratic Formula!!
Answers:
GF: x2+8x+3
FF: y = (x+.39) (x+7.61)

12. Ex. 4: Minimum and Maximum Quadratic Functions
Consider the quadratic function:
f(x) = -3x2 + 6x – 13
Determine, without graphing, whether the function has a minimum value or a maximum value.
Find the max. or min. value and determine where it occurs
Identify the function’s domain and range.

13. Ex. 4 Continued f(x) = -3x2 + 6x – 13
Begin by identifying a, b, and c.
Because a < 0, the function has a max. value. If a>0 then the function would have a min.
The max. occurs at x = -b/2a = - 6 /2(-3) = -6/-6 = 1.
The maximum value occurs at x = 1 and the maximum value of f(x) = -3x2 + 6x – 13
f(1) = -3*12 + 6*1 – 13 = – 13=-10
Plug in one for x into original function.
We see that the max is -10 at x = 1.
c. Domain is (-∞,∞) Range (-∞,-10].

14. 4b. YOU TRY!! Repeat parts a through c using the function:
f(x) = 4x2 – 16x
Answer:
Min
Min is 984 at x = 2
Domain is (-∞,∞) Range is [984,∞)

15. Summary:
Describe how to find a parabola’s vertex if its equation is expressed in vertex form.