It's an exponential graph so it must be something like [tex]y=a^x+c[/tex]
It passes through (0, -2) on the y-axis so it must be [tex]y=a^x-2[/tex]
It passes through approximately (0.5, 0) on the x-axis so
[tex]0=a^{0.5}-2[/tex]
[tex]\ln2=0.5\ln a[/tex]
[tex]\ln a= \frac{\ln2}{0.5} [/tex]
[tex]a=e^{ \frac{\ln2}{0.5}}=4 [/tex]
Equation is [tex]y=4^x-2[/tex]
