What is – 10 + (-3/4)?

Input:

14 x^2 + 57 x - 27

Plots:

Geometric figure:

parabola

Alternate forms:

(7 x - 3) (2 x + 9)

x (14 x + 57) - 27

14 (x + 57/28)^2 - 4761/56

Roots:

x = -9/2

x = 3/7

Polynomial discriminant:

Δ = 4761

Properties as a real function:

Domain

R (all real numbers)

Range

{y element R : y>=-4761/56}

Derivative:

d/dx(14 x^2 + 57 x - 27) = 28 x + 57

Indefinite integral:

integral(-27 + 57 x + 14 x^2) dx = (14 x^3)/3 + (57 x^2)/2 - 27 x + constant

Global minimum:

min{14 x^2 + 57 x - 27} = -4761/56 at x = -57/28

Definite integral:

integral_(-9/2)^(3/7) (-27 + 57 x + 14 x^2) dx = -109503/392≈-279.344

Definite integral area below the axis between the smallest and largest real roots:

integral_(-9/2)^(3/7) (-27 + 57 x + 14 x^2) θ(27 - 57 x - 14 x^2) dx = -109503/392≈-279.344

Step-by-step explanation: