Download Warm-Up

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
Lesson 3.1 Quadratic
Functions– The Three Forms

1. Standard or General Form
y = ax2+ bx + c
y-intercept
This form tells me the __________________.
crosses the y-axis
That is where the graph ________________.
(0,c)
The y-intercept is _____________________.
2. Factored Form
y = a( x – r1) (x-r2)
roots, zeros, or x-intercepts
This form tells me the __________________.
crosses the x-axis
That is where the graph ________________.
( x – r1) (x-r2) = 0
To find the roots, zeros or x-intercepts Set
_______________.
3. Vertex Form
y = a( x –h)2+k
vertex
This form tells me the __________________.
or maximum of the parabola
That is where the graphMinimum
________________.
(h,k)
The vertex is _____________________.
How to convert from different
forms?
Given:
General Form
Factored Form
Vertex Form
Given:
Factored Form
General Form
Vertex Form
Given:
Vertex Form
General Form
Factored Form
Ex. 1: y = x2-6x + 5
General Form

What form?

Factored Form
Change from general to ____________
by
Factoring
using either _______________
or
___________________.
Quadratic Formula
X2 – 6x + 5
(x-5)(x-1) = 0
X = 5, x = 1
Ex. 2: y = x2-6x + 5

Vertex form
Change from general form to __________
Completing the square
by using _________________________.
y = x2-6x + 5 Complete the square
9
9
(x2-6x + _____)
= -5 + _____
(x-3)2 -4 = y
Now Graph:
(0,5)
Y-intercept:_______
(3,-4)
Vertex :_______
(1,0)
X-intercepts: (5,0)
______, ______
Ex. 3: Using f(x) = -3x2 +6x - 13
find the vertex when given the
standard form?

Use the formula to find x :
b 

x 

2a 

In standard form a = -3, b = 6, c= -13
6
6
x

1
2(3) 6

Substitute in x to find y.
x = 1 , then y = -3(1)2 +6(1) -13 = -10
Vertex = (1, -10)
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)
Ex. 4: Minimum and Maximum
Quadratic Functions
Consider the quadratic function:
f(x) = -3x2 + 6x – 13
a. Determine, without graphing, whether the
function has a minimum value or a
maximum value.
b. Find the max. or min. value and determine
where it occurs
c. Identify the function’s domain and range.
Ex. 4 Continued
f(x) = -3x2 + 6x – 13
Begin by identifying a, b, and c.
a. Because a < 0, the function has a max. value.
If a>0 then the function would have a min.
b. 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 = -3 + 6 – 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].
4b. YOU TRY!!
Repeat parts a through c using the function:
f(x) = 4x2 – 16x + 1000.
Answer:
a. Min
b. Min is 984 at x = 2
c.
Domain is (-∞,∞) Range is [984,∞)
Summary:

Describe how to find a parabola’s vertex if its
equation is expressed in vertex form.