Parabola Formulas Summary of Day One FindingsHorizonal Parabolas

(Type 2: Right and Left)Vertical Parabolas

(Type 1: Up and Down)

Vertex Form Vertex Formkhxay 2)( hkyax 2)(

Vertex: (h, k)

Axis: x = h

Vertex: (h, k)

Axis: y = k

Opens:a (+ up; – down) Opens:a (+ right; –left)

Find VERTEX FORM EQUATION: Given Vertex & Point

Plug vertex into appropriate vertex form equation and use another point to solve for “a”.

[A] Opening VerticalVertex: (2, 4)Point: (-6, 8)

[B] Opening: HorizontalVertex: (- 4, 6)Point: (2, 8)

COMPLETING THE SQUARE REVIEWFind the value to add to the trinomial to create a perfect

square trinomial: (Half of “b”)2

[A] cxx 102[B] cxx 52

[C] cxx 82 2 [D] cxx 93 2

STANDARD FORM to VERTEX FORMMethod #1: COMPLETING THE SQUARE• Find the value to make a perfect square trinomial to the

quadratic equation. (Be careful of coefficient for x2 which needs to be distributed out)

• ADD ZERO by adding and subtracting the value to make a perfect square trinomial so as to not change the overall equation(Be careful of coefficient for x2 needs multiply by subtraction)

Example 1 Type 1: Up or Down Parabolas Write in vertex form. Identify the vertex and axis of symmetry.

[A] 862 xxy [B] 342 xxy

1a

[A] 882 yyx [B] 462 yyx

Example 2 Type 2: Right or Left Parabolas Write in vertex form. Identify the vertex and axis of symmetry.

1a

Write in standard form. Identify the vertex and axis of symmetry.

[A] 50243 2 xxy [B] 322 xxy

1aExample 3 Type 1: Up or Down Parabolas

[A] 7255 2 yyx [B] 1123 2 yyx

1aExample 4 Type 2: Right or Left Parabolas Write in vertex form. Identify the vertex and axis of symmetry.

Method #2: SHORTCUT1. Find the AXIS of SYMMETRY :

Axis equation opposite Quadratic2. Find VERTEX (h, k) of STANDARD FORM3. “a” – value for vertex form should be the same coefficient of x2 in standard form. Check by using another point (intercept)

ab

x2

ab

y2

[1] 182 xxy

PRACTICE METHOD #2: Write in vertex form. Find vertex and axis of symmetry.

[2] 20102 xxy

[3] 563 2 xxy [4] 32162 2 xxy

[5] 742 yyx [6] 452 yyx

[7] 13164 2 yyx [8] 193 2 yyx