Question

I just need the answer

Answer 1

To identify the grpah correspondig to the given function find the zeros of the function (use the quadratic formula):

`\begin{gathered} f(x)=(1)/(2)x^2+2x-6 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ a=(1)/(2) \\ \\ b=2 \\ c=-6 \\ \\ \\ x=\frac{-2\pm\sqrt[]{2^2-4((1)/(2))(-6)}}{2((1)/(2))} \\ \\ x=\frac{-2\pm\sqrt[]{4-(-12)}}{1} \\ \\ x=\frac{-2\pm\sqrt[]{16}}{1} \\ \\ x=(-2\pm4)/(1) \\ \\ x_1=-2+4=2 \\ x_2=-2-4=-6 \end{gathered}`

As the zeros are 2 and -6 the graph cross the x-axis in x=2 and x=-6

Answer: D