Answer:
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
