Answer:
Graph below
Step-by-step explanation:
Graph of the Quadratic Function
We are given the function:
[tex]y=f(x)=-x^2+8x-15[/tex]
Select 5 values of x={2,3,4,5,6}
And calculate the corresponding values of y:
[tex]f(2)=-2^2+8*2-15=-4+16-15=-3[/tex]
[tex]f(3)=-3^2+8*3-15=-9+24-15=0[/tex]
[tex]f(4)=-4^2+8*4-15=-16+32-15=1[/tex]
[tex]f(5)=-5^2+8*5-15=-25+40-15=0[/tex]
[tex]f(6)=-6^2+8*6-15=-36+48-15=-3[/tex]
We have obtained the points
(2,-3) (3,0) (4,1) (5,0) (6,-3)
Now we plot them in the graph below.
It can be noted three remarkable points:
- The vertex is located at (4,1)
- The roots are located at (3,0) and (5,0)
The roots of the equation
[tex]-x^2+8x-15=0[/tex]
Are x=3 and x=5.
