Question

use the drawing tool(s) to form the correct answer on the provided graph.plot the x - intercept(s), y - intercept, vertex, and axis of symmetry of the function\\(h(x)=(x - 1)^2 - 9\\).

Explanation:

Step1: Identify vertex form

The function is in vertex form $h(x) = a(x-h)^2 + k$, where $(h,k)$ is the vertex.
For $h(x)=(x-1)^2 - 9$, $h=1$, $k=-9$.

Step2: Find vertex

Vertex is $(h,k)$.
Vertex: $(1, -9)$

Step3: Find axis of symmetry

Axis of symmetry is $x=h$.
Axis of symmetry: $x=1$

Step4: Find y-intercept (x=0)

Substitute $x=0$ into $h(x)$.
$h(0)=(0-1)^2 - 9 = 1 - 9 = -8$
Y-intercept: $(0, -8)$

Step5: Find x-intercepts (h(x)=0)

Set $(x-1)^2 - 9 = 0$.
$(x-1)^2 = 9$
$x-1 = \pm 3$
$x=1+3=4$ or $x=1-3=-2$
X-intercepts: $(-2, 0)$ and $(4, 0)$

Answer:

• Vertex: $(1, -9)$
• Axis of symmetry: $x=1$
• Y-intercept: $(0, -8)$
• X-intercepts: $(-2, 0)$ and $(4, 0)$

To plot:

1. Mark the vertex $(1, -9)$
2. Draw the vertical line $x=1$ (axis of symmetry)
3. Mark the y-intercept $(0, -8)$
4. Mark the x-intercepts $(-2, 0)$ and $(4, 0)$
5. Sketch the parabola passing through these points, opening upwards.