Write an equation of a parabola in vertex form that passes through (7, -17) and has a vertex (4, 1)

Step-by-step explanation:

f(x) = a(x - h)² + k  - the vertex form of an equation of a parabola with vertex (h, k)

(4, 1)  ⇒  h = 4.   k = 1

f(x) = a(x - 4)² + 1   - the vertex form of an equation of the parabola with vertex (4, 1)

the parabola passes through (7, -17)  ⇒ x=7,  f(x)=-17

-17 = a(7 - 4)² + 1

-17 -1 = a(3)² + 1 -1

-18 = 9a

a = -2

The equation of the parabola in vertex form that passes through (7, -17) and has a vertex (4, 1):

                              f(x) = -2(x - 4)² + 1

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

depends on how many days you are talking about

step-by-step explanation: