Question

Consider the given function. Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of the function.

Answer 1

Answer:

Following are the solution to the gvien question:

Step-by-step explanation:  

Let the quadratic equation is:

$\to h(x) = (x + 1)^2 - 4$

vertex is:

$\to h(x) = a(x -h)^2 + k$

(h) = axis of symmetry

(h,k) = vertex.

By using the given equation:

$h(x) = (x - (-1))^2 - 4$

Hence,

$h = -1 \\\\ k = -4$

line of symmetry $x = -1$  

vertex is $(h,k) = (-1,-4)$

finding the x intercept:

 $(x + 1)^2 = 4\\\\\sqrt{(x + 1)^2} = \sqrt{4}\\\\x + 1 = \pm 2\\\\x = 2-1 \ \ \ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ \ \ \ \ \ \ \ x =-2 -1\\\\x = 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ or \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x =-3$

x -intercepts -3,1

Calculating the y-intercept when x = 0 putting into the real equation:

$h(x) = (0 +1)^2 - 4 \\\\y = 1 - 4\\\\y = -3$

Please find the graph file in the attachment.