Precalculus - Exam #1

Formulas

(X₁+X₂/2, Y₁+Y₂/2)

is the formula for finding the midpoint of a line segment.

√(X₂-X₁)² + (Y₂-Y₁)²

is the distance formula used to calculate the distance between two points.

(X-h)² + (y-k)²= r²

is the equation of a circle in standard form, where (h, k) is the center and r is the radius.

(h,k)

represents the coordinates of the center of a circle.

r

represents the radius of a circle in the equation of a circle.

(b/2)²

Completeing the square

y₂-y₁/x₂-x₁

_{Average rate of change}

(-b/2a)

Vertex

f(x+h)-f(x)/h

The difference quotient

y=|x-2|

Shifted to the right 2 units

y=|x|+1

Shifted up 1 unit

y=|x+3|

Shifted to the left 3 units

y=|x|-2

Shifted down 2 units

y=2|x|

Vertically stretched by a factor of 2

y=1/3|x|

Vertically shrunk by a factor of 1/3

y= -|x|

Reflected across the x-axis

y= |-x|

Reflected across the y-axis

1/2(b x h)

Area of triangle

R(p) = -4p²+16,000p

Solve for p using (-b/2a) to find the maximum revenue and unit price/

Solve for x and express in interval notation: 2x²>5x+12

Find the zeros, then test the inequality (true or false) and (positive or negative).

Find all the complex zeros of the function: f(z) = z⁶-126z³+125

Keep factoring the difference of cubes

a(x-h)²+k

Vertex form