Answer
See below:
Work Step by Step
Consider the quadratic function:
$f\left( x \right)=-2{{x}^{2}}+4x+5$
Now, consider the equation of the vertex for the quadratic formula.
$x=\frac{-b}{2a}$
Substitute the values in the above equation.
$\begin{align}
& x=\frac{-4}{2\left( -2 \right)} \\
& =1
\end{align}$
This shows that the vertex occurs when x is equal to1.
Substitute x as 1 in the given equation:
$\begin{align}
& y=-2{{\left( 1 \right)}^{2}}+4\left( 1 \right)+5 \\
& =-2+4+5 \\
& =7
\end{align}$
This shows that the vertex occurs at the coordinate$\left( 1,7 \right)$.
Now, substitute x as 0 in the above function to calculate the y intercept.
$\begin{align}
& y=-2{{\left( 0 \right)}^{2}}+4\left( 0 \right)+5 \\
& =5
\end{align}$
This shows that the y intercept occurs at the coordinate $\left( 0,5 \right)$.
Now, substitute y as 0 in the above function to calculate the x intercept.
$0=-2{{x}^{2}}+4x+5$
It is further solved using the quadratic function.
$\begin{align}
& x=\frac{-4\pm \sqrt{{{4}^{2}}-\left( 4\times \left( -2 \right)\times 5 \right)}}{2\times \left( -2 \right)} \\
& =\frac{-4\pm 7.483}{-4} \\
& =\frac{-4+7.483}{-4}\ \ \text{or}\ \ \frac{-4-7.483}{-4} \\
& =-0.87\ \ \text{or}\ \ \text{2}\text{.87}
\end{align}$
This shows that the x intercept occurs at the coordinate $\left( 2.87,0 \right)$and$\left( -0.87,0 \right)$.
