Answer
True statement
Work Step by Step
The equation of a quadratic function is $f\left( x \right)=a{{x}^{2}}+bx+c$, and the graph has symmetry with respect to a vertical line.
For the explanation of the statement, let’s consider $f\left( x \right)={{x}^{2}}$:
Put $x=1$ in the function,
$\begin{align}
& f\left( x \right)={{x}^{2}} \\
& f\left( 1 \right)={{\left( 1 \right)}^{2}} \\
& f\left( 1 \right)=1 \\
\end{align}$
Now, put $x=-1$ in the function,
$\begin{align}
& f\left( x \right)={{x}^{2}} \\
& f\left( -1 \right)={{\left( -1 \right)}^{2}} \\
& f\left( -1 \right)=1 \\
\end{align}$
Since f(1)=f(-1), we see that symmetry exists.
