Answer:
The graph is concave down.
y-intercept: (0, 6)
(i). x = -3 and x = 2.
Explanation:
Plotting the function gives us information about the x- and the y-intercepts.
(ii). The x - intercepts of f(x) are solutions to
[tex]-x+6-x^2=0[/tex]
The above equation is a quadratic equation, and therefore, can be solve using the quadratic formula.
Now, the quadratic formula says that if we have a quadratic equation of the form
[tex]ax^2+bx+c=0[/tex]
the solution is given by
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
Now in our case, we have
[tex]-x^2-x+6=0[/tex]
Therefore, for the quadratic formula, we have a = -1, b = -1, and c = 6; therefore,
[tex]x=\frac{-(-1)_{}\pm\sqrt[]{(-1)^2-4(-1)(6)}}{2(-1)}[/tex][tex]\Rightarrow x=\frac{1_{}\pm\sqrt[]{25}}{-2}[/tex][tex]x=-\frac{1\pm5}{2}[/tex][tex]\begin{gathered} x=-\frac{1-5}{2}=2 \\ x=-\frac{1+5}{2}=-3 \\ \end{gathered}[/tex]
Therefore, we see that the solutions to our quadratic equation ( and therefore, the x-intercepts of f(x)) are x = 2 and x = -3.
