Trig and Algebra Equations

Flashcards for trig and algebra equations

(a-b)^2?

a^2 + b^2 - 2ab

(a + b)^2?

a^2 + b^2 + 2ab

(a + b)^2 + (a - b)^2?

2(a^2 + b^2)

(a + b)^2 - (a - b)^2?

4ab

(a + b) * (a - b)?

a^2 - b^2

a^2 - b^2?

(a + b) * (a - b)

(a + b)^3?

a^3 + b^3 + 3a^2b + 3ab^3

(a - b)^3?

a^3 - b^3 - 3a^2b + 3ab^2

a^3+b^3?

(a + b)(a^2 - ab + b^2)

a^3 - b^3?

(a-b)(a^2 + ab + b^2)

Pythagorean Theorem?

opp^2 + adj^2 = hyp^2

sin^2θ + cos^2θ?

1 in the terms of sin and cos.

1 - sin^2θ?

cos^2θ

1 - cos^2θ?

sin^2θ

1 + cot^2θ?

csc^2θ

csc^2θ - cot^2θ?

1in terms of csc.

1 + tan^2θ?

sec^2θ

sec^2θ - tan^2θ?

1 in terms of tan

Discriminant

b²-4ac

Product of Roots

α*β = c/a

Parabola

The shape of the graph of a quadratic function

Axis of symmetry

The line that divides a parabola into two matching halves

y-intercept

the y-coordinate of a point where a graph crosses the y-axis

Roots of Parabola

The point(s) where a graph intersects the x-axis

Vertex

The highest / lowest point on the parabola (peak)

Maximum

The highest point of a parabola

Minimum

the lowest point of a parabola

Concavity

when a parabola opens up or open down

Roots of a quadratic equation

alpha and beta and two roots

Sum of Roots

α + β = -b/a

Axis of symmetry formula

x = - b / 2a (derived from y=ax²+bx+c)

Axis of symmetry from roots

(α + β) / 2