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PaTYTxmykOSyqYtuCUnX

Study note

Stephanie💜

United States of America

DEFAULT (US)

Algebra 1

Algebra 2

Quadratic Functions in Standard Form

Quadratics

Intro to parabolas

D
8
Warm-Up
1. The standard form of a quadratic function is
f(x) = ax 2 +bx+c
Identify the values of a, b, and C in:
f(x) = 3x²-bx+5
a = 3
b = -b
c= 5
2. Given that f(x) = 3x² - 6x +5
Find the values of
f(0)
3(0)²-6(0) +5=5
f(1): 3 (1) ² - 6(1) + 5 = 2
f(-1): 3(-1)-6(-1) +5=14
etry QUADRATIC FUNCTIONS IN STANDARD FORM
f(x)
= ax² + bx +C
The y-intercept is
(0,8)
Finding the Vertex (h,k) :
•
h=-b
29
To find K, substitute the value of h in the function.
Equation of axis of symmetry is the same
h
7
Example
Graph: f(x) = 3x² - 6x + 5
Find:
a vertex
c) y-intercept
1st Vertex
h = -b
29
(hik)
h = -(-6)
2 (3)
b = 1
b.) axis of symmetry.
d) Domain
and
29
Substitute h to find k
f(1) = 3(1) 6 (1) +5
f(1) = k = 2
Vertex: V (1,2)
as
range
2nd y-intercept
Substitute x = 0
y - Intercept: (0,5) Graph
f(x) = 3x² - 6x + S
a) Vertex
b.) Axis of symmetry x = 1
c) y-intercept: (0,5)
d) Domain
>
V(1,2)
←
: All real numbers
Range: y2 2
a
[2,00)
y int
minimum
This function has
3rd step: Find a reflected point over the axis of symmetry
to
-8
6
4
-2
-2
+10
12
which is
2
(-8, 8)
- vertex
(2,5) 3rd step
T +
4
6
2
T
8
10 ;
is
A ZERO OF A FUNCTION
an x-valve
that makes f(x)=0, A zero of a function.
is an x-intercept
Ex. Find the x-intercepts of f(x)=x² - 4x + 3
0=x² - 4x + 3
0= (x-1)(x-3)
|x-1=0
X= |
(1,0)
y-int. : (0,3)
h= -b
2 a
or
Find the Vertex
(h, k)
x-3=0
x=3
(3,0)
k
2
h=-(-4)
2 (₁)
-
k= (2) ²4 (2) + 3
48+3
4
-4.
4 h = 2
2
4
6
8
Vertex:
(2,-1)

Quadratic Functions in Standard Form

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Quadratic Functions in Standard Form

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying