The Solution:
Given:
[tex]g(x)=x^2+10x-7[/tex]
We are required to find the key features of the given function.
Below is the graph of the function:
Thus, the correct answers are:
[tex]The\text{ vertex}=\text{ minimum }(-5,-32)[/tex][tex]Axis\text{ of symmetry: }x=-5[/tex][tex]The\text{ y-intercept}:\:\left(0,\:-7\right)[/tex]
The x-intercepts are:
[tex]\begin{gathered} \mathrm{X\:}-i\mathrm{ntercepts}:\:\left(-5+4\sqrt{2},\:0\right),\:\left(-5-4\sqrt{2},\:0\right), \\ Or \\ X-intercepts:\text{ }(-10.657,0),\text{ }(0.657,0) \end{gathered}[/tex]
