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.
delete undo reset

Explanation:

Step1: Identify vertex from vertex form

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

Step2: Find x-intercepts (set $h(x)=0$)

$$\begin{align*} (x+1)^2-4&=0\\ (x+1)^2&=4\\ x+1&=\pm2 \end{align*}$$

Solve for $x$:
$x+1=2 \implies x=1$; $x+1=-2 \implies x=-3$.
So x-intercepts are $(1,0)$ and $(-3,0)$.

Step3: Find y-intercept (set $x=0$)

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

So y-intercept is $(0,-3)$.

Step4: Identify axis of symmetry

For vertex form $a(x-h)^2+k$, axis of symmetry is $x=h$. Here $h=-1$, so axis is $x=-1$.

Answer:

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