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CTS Notes on Parabolas in Algebra II: Finding Vertex, Axis of Symmetry, and Focal Points, Study notes of Algebra

These notes provide instructions on how to find the vertex, axis of symmetry, direction of opening, and focal points of parabolas represented by quadratic equations. The notes include examples for the equations y = x²z, 6x + 6, and y = 2x² + 16x + 35, as well as instructions for writing the quadratic equation in staar form and graphing the parabola. The document also includes a diagram for the equation 4x - 13 - y² + 2y = 0.

What you will learn

  • How do you find the vertex of a parabola given its quadratic equation?
  • What is the axis of symmetry for the parabola y = x²z, 6x + 6?
  • How do you graph the focus and directrix of a parabola?

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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Algebra II
Parabolas CTS Notes
Write each quadratic equatioh i
following parts of the parabola
1 y=xZ 6x+6
Per
find the
f
/
f,
STAAR form:
l! Z ' .//
axis of symmetry ÿ ;'''
;% + 2
direction of opening', {Z )
focal width: I
STAAR form: ÿ \ riÿÿ 'I;1 1
vertex', ÿi!, % ÿ'
"I '::+. 1
axis of symmetry:
direction of opening !ÿiiÿ;
focal width
3. y=2x2+16x+35
LO
' }
.
,
i I )
STAAP, form:
vertex: ( 'ÿ! , ':,:ÿ)I
axis of symmetry: ){ ÿ
• P,
direction of opening:
li, ,ÿ
focal width: ÿ
-4
vertex:_ (; Z i ) ,4
axis of symmetry: ,ÿ,. ÿ#'
direction of optening:d i{> !ÿ ÿi
focal width: ,ÿ
pf2

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Algebra II

Parabolas CTS Notes

Write each quadratic equatioh i

following parts of the parabola

1 y=xZ 6x+

Per

find the

f /

f,

STAAR form:

l! Z ' .//

axis of symmetry (^) ;%ÿ ;''' + 2

direction of opening', {Z )

focal width: I

STAAR form: ÿ \ riÿÿ 'I;1 1

vertex', ÿi!, % ÿ'

"I '::+. 1 axis of symmetry:

direction of opening !ÿiiÿ;

focal width

  1. y=2x2+16x+

LO

' }

.

,

i I )

STAAP, form:

vertex: ( 'ÿ! , ':,:ÿ)I

axis of symmetry: ){ ÿ

  • P, direction of opening: li, ,ÿ

focal width: ÿ

vertex:_ (; Z i ) ,

axis of symmetry: ,ÿ,. ÿ#'

direction of optening:d i{> !ÿ ÿi

focal width: ,ÿ

Write the quadratic equation in STAAR form by completing the square and then graph the

parabola. Also graph the vertex, axis of symmetry, focus, and directrix.

. 4x - 13 - y2 + 2y = 0

i

J

I ;

i

--+--

1----+---- I

T

....

i i i i

i i i

pÿ

, 8y + 26 l- -2xz + 20x

oE I IE I I I I ,_ÿ [ I I I I

I I

12 I I I I

12 I I I

,[2 t I I

axis of symmetry: Iÿ

direction of opemng: ÿ: i:i ÿ/:ÿ:= ÿ/ÿ

focal width: