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: h

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x