91影视

Function -$f\left(x\right)=-2x^2+2x-3$

Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.

Remind yourself that the quadratic function is given by - $f\left(x\right)=a{x}^2+bx+c,a鈮�0$

Since role="math" localid="1646670037508" $a<0$,We can conclude that the function open downwards. we are looking the vertex as $[-\frac{b}{2a},f(-\frac{b}{2a}\left)\right]$, Lets us find the vertex.

$-\frac{b}{2a}=-\frac{2}{2(-2)}$

$-\frac{b}{2a}=0.5$

role="math" localid="1646670773819" $$\begin{gathered} f(-\frac{b}{2a})=f(0.5) \\ f(-\frac{b}{2a})=-2脳0.5^2+2脳0.5-3 \\ f(-\frac{b}{2a})=-0.5+1-2 \\ f(-\frac{b}{2a})=-2.5 \end{gathered}$$

Vertex is - (0.5, -2.5)

Determine the Axis of symmetric -

$$\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{2}{2(-2)} \\ x=0.5 \end{gathered}$$

The axis of symmetric passes through the vertex of the function and is parallel to the y-axis.

Determine the point atwhich the function intersects the x-axis -

$$\begin{gathered} f\left(x\right)=0 \\ -2x^2+2x-3=0 \end{gathered}$$

This function does not intersect the x-axis.

Determine the point at which the function intersects the y-axis -

$$\begin{gathered} f\left(0\right)=-2脳0^2+2脳0-3 \\ f\left(0\right)=-3 \end{gathered}$$

The point at which the function intersect the y-axis is -

$y=-3$

Function - $f\left(x\right)=-2x^2+2x-3$

Determine the domain and the range of the function.

• The Domain is - $\mathrm{鈩�}$
• And the range is - $y鈭�(-鈭�,-2.5]$
  

Function - $f\left(x\right)=-2x^2+2x-3$

Determine where the function is increasing and where it is decreasing.

Function increasing for - $x鈭�(-鈭�,0.5]$

Function decreasing for -$x鈭�[0.5,+鈭�)$

The graph of function will be -