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