Vertex Form

A value is the same in each form

y = a(x-r)(x-s)

Special occasions

When converting from Vertex form to factored form, if the number you are square rooting is negative, then there are no zeros (no factored form). The vertex is either above the x-axis and opening upwards, or it is below and opening downwards.

Example

y = 2/3(x-3)^2 + 5
0 = 2/3(x-3)^2 + 5
-5 = 2/3(x-3)^2
(-5)/(2/3) = (2/3(x-3)^2)/(2/3)
-7.5 = (x-3)^2
cannot square root -7.5, therefore there are no zeros

y = ax^2 + bx + c

y = 2/3(x-3)^2 + 5

Expand (x-3)^2
y = 2/3(x-3)(x-3) + 5
Multiply (x-3)(x-3) using FOIL
y = 2/3(x^2 - 3x - 3x + 9) + 5
combine like terms in brackets
y = 2/3x^2 - 4x + 6 + 5
combine like terms
y = 2/3x^2 - 4x + 11

Take value c to other side

Divide both sides by value a

Square root both sides

Solve for x

Don't forget the positive and negative roots

When writing the Factored form with the x-int, r and s are equal to x-ints but the opposite signs (if the x-int is positive,it will be -r or -s, if x-int is negative, it will be +r or +s)

Remember to use samdeb and not bedmas
when factoring

y = 4(x-1)^2 - 6

0 = 4(x-1)^2 - 6
6 = 4(x-1)^2
6/4 = (4(x-1)^2)/4
1.5 = (x-1)^2
sqrt + or - 1.5 = sqrt (x-1)^2
1.22 (rounded) = (x-1)
1.22 + 1 =x
x = 2.22
-1.22 = (x-1)
-1.22 + 1 = x
x = -0.22

x ints are = 2.22 and -0.22
y = 4(x-2.22)(x+0.22)