Algebraic techniques

aⁿ =???

a x a x a the amount being the number of ‘n’

a^ya^x =???

a^x+y

a^x/a^y =???

a^x-y

(a^x)ⁿ = ???

a^xn

a^m/n = ???

ⁿ√a^m

(ab)^x = ????

a^xb^x

(a/b)^x = ????

a^x/b^x

a⁰ = ???

1

a^-n= ??? for postive integers

1/aⁿ

a^-n

1/^m√aⁿ

√a/√b = ???

√a/b

(√a)² = ???

(a^1/2)²

= a¹

= a

(b√a)² = ???

b²a

√a + √a = ??

2√a

√a/√b x √b/√b = ???

√ab/√b

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Find intercepts: y = x² -2x -8

ƒ(0) = (0)² -2(0) -8

y int: = -8

x²-2x-8 = 0

(x+2) (x-4) = 0

x int: -2, 4

Discriminent formula and the nature of roots

√b²-4ac

∆ = 0 → 2

∆ > 0 → 2

∆ ∠ 0 → no x-intercepts

Forumla of a circle at (0,0)

x² + y² = r²

Formula of a circle when on an axis

(x-a)² + (y-b)² = r²

Draw √r²-x²

Draw y = -√r²-x²

Draw x = √r²-y²

Draw x = -√r²-y²

Effects of the coefficient:

Larger number = skinner

a = 1 → normal curve

a = fraction → wider

Finding minimum or max point formula

-b/2a

Exponential forumla:

y = ax²

Graphed: y = 2^x

Graphed y = 2^-x

Graphed y = -2^x

Graphed y = -2^-x

Simplify 1000^-2/3

1/(³√1000)²

1/(10)²

1/100