Algebra II Honors Midterm Review

Arithmetic Sequence Recursive Rule

a(1)=_, a(n) = a(n-1) + d, n ≥ 2

Arithmetic Sequence Explicit Rule

a(n) = a(1) + (n-1)d

Arithmetic Series Finite Formula

S(n) = n(a(1)+a(n)/2)

Arithmetic Series Infinite Formula

Diverges (not possible)

Geometric Sequence Recursive Rule

a(1) = _, a(n) = (a(n-1))(r), n ≥ 2

Geometric Sequence Explicit Rule

a(n) = a(1)(r^n-1)

Geometric Series Finite Formula

S(n) = a(1)(1-r^n)/1-r

Geometric Series Infinite Formula

If |r|<1, then the series converges to S(n) = a(1)/1-r ; If |r| ≥ 1 then the series diverges (not possible)

If f(-x) = f(x), then f(x) is _

even

Even functions are symmetric over the _

y-axis

If f(-x) = -f(x), then f(x) is _

odd

If f(-x) ≠ f(x) ≠ -f(x), then f(x) is _

neither even nor odd

Linear Parent Function

Quadratic Parent Function

Cubic Parent Function

Square Root Parent Function

Absolute Value Parent Function

a(x−h)^2+k

Left/Right

If h>0, the shift is to the right, and if h<0, the shift is to the left.

a(x−h)^2+k

Vertical Stretch/Compression

If a>0, the parabola opens upwards. If a<0, the parabola opens downwards.

a(x−h)^2+k

Up/Down

If k>0, the shift is up, and if k<0, the shift is down.

Difference of Two Squares

a²-b²=(a+b)(a-b)

Sum of Two Cubes

a³+b³=(a-b)(a²-ab+b²)

Difference of Two Cubes

a³-b³=(a-b)(a²+ab+b²)

Quadratic Formula

-b±√b²-4ac/2a

Vertex form

a(x−h)²+k

Standard Form

y=ax² + bx + c

x-value of a vertex

-b/2a