91Ó°ÊÓ

The graph of $f\left(x\right)=a{x}^2+bx+c,a≠0$

opens up and has a minimum value when $a>0$, and

opens down and has a maximum value when $a<0$

The given function is $f\left(x\right)=3x^2+4x-5$

In the function $f\left(x\right)=3x^2+4x-5$, we have $a=3>0$

So, the graph of function $f\left(x\right)=3x^2+4x-5$ opens up and has a minimum value.

The graph of $f\left(x\right)=a{x}^2+bx+c,a≠0$

opens up and has a minimum value when $a>0$, and

opens down and has a maximum value when $a<0$

The given function is $f\left(x\right)=-2x^2+9$

In the function$f\left(x\right)=-2x^2+9$, we have $a=-2<0$

So, the graph of function $f\left(x\right)=-2x^2+9$ opens down and has a maximum value.

The graph of $f\left(x\right)=a{x}^2+bx+c,a≠0$

opens up and has a minimum value when $a>0$, and

opens down and has a maximum value when $a<0$

The given function is $f\left(x\right)=-5x^2-8x+2$

In the function $f\left(x\right)=-5x^2-8x+2$, we have $a=-5<0$

So, the graph of function $f\left(x\right)=-5x^2-8x+2$ opens down and has a maximum value.

The graph of $f\left(x\right)=a{x}^2+bx+c,a≠0$

opens up and has a minimum value when $a>0$, and

opens down and has a maximum value when $a<0$

The given function is $f\left(x\right)=6x^2-5x$

In the function $f\left(x\right)=6x^2-5x$, we have $a=6>0$

So, the graph of function $f\left(x\right)=6x^2-5x$ opens up and has a minimum value.