Question

Create a hand drawn sketch of the quadratic function: h(x)= x^2 -5x-6To earn full credit be sure to identify the vertex, the axis of symmetry and all intercepts. Include all work, calculations and steps needed (as described in this lesson) to create the graph.Let your teacher know if you have any questions on how to upload or share your written work.

Answer 1

$h(x)=x^2-5x-6$

1. Find the axis of symmetry: Use the next formula:

$\begin{gathered} f(x)=ax^2+bx+c \\ \text{axis of si}mmetry\colon \\ x=-\frac{b}{2a} \end{gathered}$$\begin{gathered} x=-\frac{-5}{2(1)} \\ \\ x=\frac{5}{2} \\ \\ x=2.5 \end{gathered}$

Axis of symmetry: x=2.5

2. Find the vertex: x-coordinate of the vertex is the value of the axis of simmetry, use it to find the y-coordinate of the vertex:

$\begin{gathered} h(\text{2}.5)=(2.5)^2-5(2.5)-6 \\ h(\text{2}.5)=6.25-12.5-6 \\ h(2.5)=-12.25 \end{gathered}$

Vertex: (2.5, -12.25)

3. x-intercepts: Equal the function to 0 and solve x:

$\begin{gathered} x^2-5x-6=0 \\ \\ \text{Factor:} \\ x^2+x-6x-6=0 \\ x(x+1)-6(x+1)=0 \\ (x+1)(x-6)=0 \\ \\ \text{Solve x:} \\ x+1=0 \\ x=-1 \\ \\ x-6=0 \\ x=6 \end{gathered}$

x-intercpets: (-1,0) and (6,0)

4. Find y-intercept: Evaluate the function when x=0:

$\begin{gathered} h(0)=0^2-5(0)-6 \\ h(0)=0-0-6 \\ h(0)=-6 \end{gathered}$

x-intercept: (0,-6)

5. Graph: