Answer:
the function has two real roots and crosses the x axis in two places.
Step-by-step explanation:
Using the general quadratic formula;
[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
for a quadratic equation
[tex]ax^2 +bx+c=0[/tex]
given the quadratic function below;
[tex]G(x) = -x^2 +4x+2[/tex]
the roots of the equation can be calculated by applying the quadratic formula.
[tex]x = \frac{-4\pm \sqrt{4^2 -(4*-1*2)}}{2*-1}\\x = \frac{-4\pm \sqrt{16 -(-16)}}{-2}\\x = \frac{-4\pm \sqrt{32}}{-2}\\x = 4.449 \\or\\x = -0.449\\[/tex]
Therefore, the function has two real roots and crosses the x axis in two places.
Attached is the graph of G(x) for more understanding.
