Name: Knowunity
Brand: Knowunity

English (US)

quadratic formula, factoring, zero product property, taking a square root, completing the square, axis of symmetry 

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Study note

lily

United States of America

DEFAULT (US)

DEFAULT

Algebra 2

Solving and Graphing Quadratic Equations

Overview

02: Solving quadratic equations
Def: f(x) = AX²+BX+C
A, B, C = TR
O quadratic formula
* solve =
isolated vanable
-> x==b+√√√b² - 4ac
(**
za
Prerequesite Ax²+BX+C =0
part of quadradic-discriminanti √²-496
is tell how many solutions x has
if real
if D=0, then I real solution.
if D²0, then o real solutions
graph of quadratic -> palabra:
平平平
Factoring / Zero Product Property
²+8×2-15
+3)(+5)=0
if have 2 nombiers tha
if goh =0 then either gor hisok
eimer x+3 or x+b=0
X=-3, -5
Take a Square Rat
4x²-6-0
√4x²√√G
2x=+√6 or 12x1= √6
x=+√√6
2
(4) completing the Square
perticulary square trinomial
ex: x² + 4x + 4 -> (x+2) ²
ex: xr₂6vrg ->(x+3)²
ex:
✓²-19x 181 → (*.9²
can make any trinomial perfect squared
AX²+bx+C (trinomial)
general form
+ bx + ( )² = (x + ²)² (4₁
UZ: Solving Quadratic Equations Continued
ex: x² +8x-2=0
x²+8x=2
X²+8+16=18
√(x+4)²√18
x+4=18
X=44518
* memod 4 might involve method 3
U2: Quadratic Funchon
f(x) = ax²+bx tc
ostpot where
Verley form: F(x) = a (x-h) ²+k₁
w/ perfect square trinomial.
factured Form: f(x) = a (bxtc) (@xte).
Standard: f
Vertex.
f(0) = C → yant f(x)=3(x4) — 2
W
(o, c)
= standard form
bic are TR
CAI
show y intercept, aos
U2: Axs of Symmetry
by line X-
12 vertical line
venex is on axis
a 40,
a=o not quadratic
(0,1)
f219129
hand kane points
of vertex
.agg
-1² =(x-1)² = solate square
- from Standard form
na is the
leading coeffecient
02. Graphing Practice
(F(x) = -2x³-8x+1 (stanclarel)
h, k R
A
y int -1,
axis of symmemy: x = 20/22/²/² = -2
vertex (-29)
Factored Form
y=(x+) (3x-1)
0=(2x+1)(3x²-1)
show x-intercepts
+
Vertex on dotted line
split falabla in half
vertex equation.
-2(-2)²-8 (-23+1
-8 + 16+1 =9
(find y point in vertex).

Solving and Graphing Quadratic Equations

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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.

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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

Solving and Graphing Quadratic Equations

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