Question

use the drawing tool(s) to form the correct answers on the provided graph. consider the given function. $h(x) = (x + 1)^2 - 4$ plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of the function. drawing tools select mark feature line click on a tool to begin drawing

Explanation:

Step1: Identify vertex from vertex form

The function is in vertex form $h(x) = (x-h)^2 + k$, where $(h,k)$ is the vertex. Here $h=-1$, $k=-4$, so vertex is $(-1, -4)$.

Step2: Find axis of symmetry

Axis of symmetry is $x=h$, so $x=-1$.

Step3: Calculate x-intercepts (set $h(x)=0$)

$$(x+1)^2 - 4 = 0$$
$$(x+1)^2 = 4$$
$$x+1 = \pm 2$$
$x+1=2 \implies x=1$; $x+1=-2 \implies x=-3$.
So x-intercepts are $(1,0)$ and $(-3,0)$.

Step4: Calculate y-intercept (set $x=0$)

$$h(0) = (0+1)^2 - 4 = 1 - 4 = -3$$
So y-intercept is $(0, -3)$.

Answer:

• Vertex: $(-1, -4)$
• Axis of symmetry: Vertical line $x=-1$
• X-intercepts: $(1, 0)$ and $(-3, 0)$
• Y-intercept: $(0, -3)$

To plot:

1. Use "Mark Feature" to place points at $(-1, -4)$, $(1, 0)$, $(-3, 0)$, $(0, -3)$
2. Use "Line" to draw the vertical line $x=-1$