Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of the function. h(x)=(x+1)^2-4

see explanation

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

h(x) = (x + 1)² - 4 is in this form, hence

vertex = (- 1, - 4)

the axis of symmetry passes through the vertex is vertical with equation

y = - 1 ← axis of symmetry

To find the y- intercept let x = 0 in the equation

h(0) =(0 + 1)² - 4 = 1 - 4 = - 3 ⇒ (0, - 3) ← y- intercept

to find the x-intercepts let y = 0 in the equation, hence

(x + 1)² - 4 = 0 ( add 4 to both sides )

(x + 1)² = 4 ( take the square root of both sides )

x + 1 = ± 2 (subtract 1 from both sides )

x = - 1 ± 2 ⇒ x = - 1 - 2 = - 3, x = - 1 + 2 = 1, hence

(- 3, 0), (1, 0 ) ← x- intercepts

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: