Determine whether $f(x)=7x^2+14x-9$ has a minimum or maximum value. Find the value of the minimum or maximum. Find the axis of symmetry.
$f(x)$ has a :
minimum
maximum

The value of the minimum or maximum is: $◻$ help (numbers)
The axis of symmetry for $f(x)$ is given by $x=◻$ help (numbers)

Step 1 ：The function $f(x)=7x^2+14x-9$ is a quadratic function. The general form of a quadratic function is $f(x)=a{x}^2+bx+c$. If the coefficient $a$ is positive, the function has a minimum value. If the coefficient $a$ is negative, the function has a maximum value. In this case, the coefficient $a$ is 7, which is positive. Therefore, the function has a minimum value.

Step 2 ：The value of the minimum or maximum of a quadratic function $f(x)=a{x}^2+bx+c$ is given by $f(-\frac{b}{2a})$. So, we can substitute $-\frac{b}{2a}$ into the function to find the minimum value.

Step 3 ：The axis of symmetry of a quadratic function $f(x)=a{x}^2+bx+c$ is given by $x=-\frac{b}{2a}$. So, we can calculate $-\frac{b}{2a}$ to find the axis of symmetry.

Step 4 ：Substituting $-\frac{b}{2a}$ into the function, we find that the minimum value is -16.

Step 5 ：Calculating $-\frac{b}{2a}$, we find that the axis of symmetry is -1.

Step 6 ：Final Answer: The function $f(x)=7x^2+14x-9$ has a minimum value. The value of the minimum is $\boxed{{\displaystyle -16}}$. The axis of symmetry for $f(x)$ is given by $x=\boxed{{\displaystyle -1}}$.