91影视

First, separate the xterm from the constant and factor, we get:

$$\begin{gathered} f\left(x\right)=-2x^2+8x-7 \\ f\left(x\right)=-2\left(x^2-4x\right)-7 \end{gathered}$$

Now, Take half of $-4$and then square it, we get:

${\left(\frac{1}{2}路-4\right)}^2=4$

So $4$will complete the square.

The constant $4$completes the square and then we have to subtractrole="math" localid="1645344192576" $-2脳4=-8$ from the constant.

role="math" localid="1645344253597" $$\begin{gathered} f\left(x\right)=-2\left(x^2-4x\right)-7 \\ f\left(x\right)=-2\left(x^2-4x+4\right)-7-(-8) \\ f\left(x\right)=-2{\left(x-2\right)}^2+1\_\_\_\_\left(1\right)\left[{\left(a-b\right)}^2=a^2-2ab+b^2\right] \end{gathered}$$

From the equation (1), we get:

$$\begin{gathered} a=-2 \\ h=2 \\ k=1 \end{gathered}$$

Since the value of $a$ is negative then it is a downwards parabola

The vertex of the parabola from the equation is given as:

$\left(h,k\right)=\left(2,1\right)$

Substituting $x=0$in the equation (1), we get:

$$\begin{gathered} f\left(x\right)=-2{\left(x-2\right)}^2+1 \\ f\left(0\right)=-2{(0-2)}^2+1f\left(0\right)=-2\left(4\right)+1 \\ f\left(0\right)=-8+1 \\ f\left(0\right)=-7 \end{gathered}$$

They- intercept is $\left(0,-7\right)$

The point symmetric toy-intercept across the axis of symmetry is$\left(4,-7\right)$

Substituting $f\left(x\right)=0$in the equation (1), we get:

role="math" localid="1645345218405" $$\begin{gathered} f\left(x\right)=-2{\left(x-2\right)}^2+1 \\ 0=-2{(x-2)}^2+1-1=-2{\left(x-2\right)}^2 \\ {\left(x-2\right)}^2=\frac{1}{2} \\ x-2=卤\sqrt{\frac{1}{2}} \\ x=卤\frac{1}{\sqrt{2}}+2 \end{gathered}$$

$$\begin{gathered} x=\frac{1}{\sqrt{2}}+2 \\ x=2.707 \end{gathered}$$

or

$$\begin{gathered} x=-\frac{1}{\sqrt{2}}+2 \\ x=1.292 \end{gathered}$$

So, the x-intercept is $\left(2.707,0\right)$and $\left(1.292,0\right)$

Using all the properties of the function, the graph is given as: