we are given
[tex]y=10-x^2+3x[/tex]
Table:
we can select any random values of x and find y
At x=-2:
[tex]y=10-(-2)^2+3(-2)[/tex]
[tex]y=0[/tex]
At x=-1:
[tex]y=10-(-1)^2+3(-1)[/tex]
[tex]y=6[/tex]
At x=0:
[tex]y=10-(0)^2+3(0)[/tex]
[tex]y=10[/tex]
At x=1:
[tex]y=10-(1)^2+3(1)[/tex]
[tex]y=12[/tex]
At x=2:
[tex]y=10-(2)^2+3(2)[/tex]
[tex]y=12[/tex]
Graph:
x-intercept:
we can set y=0
and then we can solve for x
[tex]0=10-x^2+3x[/tex]
[tex]10-x^2+3x=0[/tex]
[tex]x^2-3x-10=0[/tex]
[tex](x-5)(x+2)=0[/tex]
so, we get
[tex]x=-2,x=5[/tex]
y-intercept:
we can plug x=0 and find y
[tex]y=10-(0)^2+3(0)[/tex]
[tex]y=10[/tex]
