Step 1
Given;
[tex]y=-x^2+10x-24[/tex]
Required; To graph the function.
Step 2
Graph the parabola showing the vertex with two points to the left and the right of the vertex respectively.
[tex]\begin{gathered} \text{For the vertex(h,k); } \\ h=-\frac{b}{2a} \\ b=10 \\ a=-1,c=-24 \\ h=-\frac{10}{2(-1)} \\ h=-\frac{10}{-2} \\ h=5 \\ k=\frac{-D}{4a} \\ D=b^2-4ac \end{gathered}[/tex][tex]\begin{gathered} D=(10)^2-(4(-1)(-24)) \\ D=100-96 \\ D=4 \\ k=\frac{-4}{4(-1)}=\frac{-4}{-4}=1 \\ \text{The vertex, (h,k)=(5,1)} \end{gathered}[/tex]
Step 3
Two points to the right
[tex]\begin{gathered} when\text{ x=6} \\ y=-(6)^2+10(6)-24 \\ y=-36+60-24 \\ y=0 \\ when\text{ x=8} \\ y=-(8)^2+10(8)-24 \\ y=-64+80-24 \\ y=-8 \\ \text{The two points are;} \\ 1)_{}(6,0) \\ 2)(8,-8) \end{gathered}[/tex]
Step 4
Two points the left
[tex]\begin{gathered} When\text{ x=4} \\ y=-(4)^2+10(4)-24 \\ y=-16+40-24=0 \\ \text{when x=}2 \\ y=-(2)^2+10(2)-24 \\ y=-4+20-24=-8 \\ \text{The two point are;} \\ 1)(4,0) \\ 2)(2,-8) \end{gathered}[/tex]
Step 5
Plot the graph
