Day 107 Converting Between Forms of Quadratic Equations
To convert a function from standard form to intercept
Standard Form to Intercept Form
form, you j ust need to
"fACTt)l2_
Convert to intercept form and state the z~ os.
1. y
.
rYl
= x 2 - 3x - 18 _ \ ~
x -Co)(x t 3) -le>,1
f"-i
...
'3
j:: (
2-eJU>S: ( Co,()) ~ (-3,o)
3.
= x2 -
+ 9 -~'\--...
~; (')(-?,)()(-3
4. y = x2
Si - ~
11: cx-sJCx+s"''l
s-. S,b) ( ... s,b)
-
6x
~:(3,o
To convert a func 10n ram mte cept_ o
_r~m-:ct o standard form, you
Intercept Form to Standard Form
justneed to
rnuL-hpl~
,
(Fol L/ 130;><)
= (x
+ 1)( )(+ I
'2+X+ x+f
u= x'l.+ax+l
...j
To convert a function from vert
Vertex Form to Standard Form
just need to
001.d:lip ~
\(\-{.: (0 ,l )
form to standard form, you
and combine
h161 -1-~rmr
Convert to standard form .
~
2.y ~~t+,
~ 3-x -3x+ll_t
::- ~ x-i.-<ox + 10
4. y = (x
+ 2) 2
--------------~--- ~
(x-+:0~~~-~,~--------s-\-Ot\do..rc.l
~M
L)(.+1l(x-1-l\-1lo
xa411)(+\14-~
j" '>(;;(4-'a)t-15
'\(\~
~fr\
;(X.+S)(X-J-1 1
~
Name: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Date: _ _ _ _ _ _ _ _ Period: _ _
HW: Quiz #20 Review Worksheet
Day 107 Writing Quadratic Function Notes
When writing ~uadratic functions using given information, it is important to first determine
Lohlch ~ -lo f•l tp
.
Remember what each form tells you about the function.
Standard Form
2
f(x) = ax + bx+ c
a.= lJ.)icHh/cCOr\Ol\11·~
C,:. ~ it'\l
1.
Vertex Form
Intercept Form
2
f(x) = a(x - h) + k
...
f(x) = a(x - p)(x - q)
'r
(h I Kl -= vtr~
I
--
\.
/'
w.o) - X _.,t'1S
~
~,t>'\
ar
1:e<OS'
Write
2. Write an equation of a quadratic function that opens down and has zeros of (-2, 0) and
(5, O).
·,I\W"Ct2f'~
3.
:r -3(x-n.>
(x-s)
Write an equation of a quadratic function that opens down, is more narrow than
y
x 2 , and has vertex of ( -5, 7).
=
'IJefVJ-/>
~:: - ;).. (x+s)'J. t t
4. Write an equation of a quadratic function that opens up, is wider than y =
x-intercepts of (3, 0) and (-9, O).
x 2 , and has
Name: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
~
Date: _ _ _ _ _ _ _ _ __
Period: _ __
Day 107 Homework: Review for Vertex and Intercept Form Quiz
No Calculator on this side of the homework!
Given the following equations in vertex form, indicate the vertex.
+1
1. y=7(x-11)2-7
2. y=iCx+3) 2 +25
3. y = 5(x - 9) 2
Vertex:------
Vertex: _ _ _ _ __
Vertex:------
Given the following equations in intercept form, indicate the zeros.
= 3(x -
4. y = -2(x + 9)(x - 3)
5. y
2)(x - 15)
Zeros: _ _ _ _ __
Zeros:------
6. y = 6(x
+ 7)(x + 11)
Zeros:------
Write the equation given the description.
8. the vertex is (-5, 8) and wider than y = x 2
(', 7. opens down and the vertex is (7, -9)
Vertex Form: _ _ _ _ _ _ _ _ _ __
Vertex Form:
9. zeros are (2, O) and (-7, O) narrower than y = x 2
10. Opens up and the zeros are (-4, 0) and (-8, O)
Intercept Form: _ _ _ _ _ _ _ _ _ __
Intercept F o r m : - - - - - - - - - - -
Find the axis of symmetry for each:
11. f(x) = 3x 2
-
12x + 5
12. y = (x - 1)(x + 5)
-----------
Calculator ALLOWED on this side of the homework.
13. Convert to standard form: f(x) = 3(x + 2)(x - 6)
14. Convert to intercept form and identify the zeros: f(x)
15. Given f(x) = 2x 2 - 4x
= 4x 2 + 8x -
40
+ 5 Find the vertex and write in vertex form.
=
16.. The equation h(t)
-12t 2 + SOt + 10, where his the height in feet and t is time in seconds, models V
the path of an object in flight. Use that equation to answer the following questions. You do not have to show
work.
y
a. What is the starting height of the object?
b. What is the object's maximum height?
c. When does the object hit the ground?
e. Graph the path of the object using the information above.
Be sure to label and number your axes.