Graph the quadratic function. $$f ( x ) = - x ^ { 2 } - 3 x + 2$$

Question

Quizplus · Accepted Answer

We can find the vertex of the quadratic function using the formula $x=-\frac{b}{2a}$ and then plot the vertex and another point to sketch the parabola.
In this case, $a=-1$, $b=-3$, and $c=2$.
So, $x=-\frac{-3}{2(-1)}=\frac{3}{2}$ is the x-coordinate of the vertex.
To find the y-coordinate, we substitute $x=\frac{3}{2}$ into the function and get $f(\frac{3}{2})=-\frac{1}{4}$.
Therefore, the vertex is at $\left(\frac{3}{2},-\frac{1}{4}\right)$.
Plotting this point and another point, we get the graph:

![Graph of f(x)=-x^2-3x+2](https://i.imgur.com/9Itqi1S.png)

So, the answer is (C).

Graph the Quadratic Function f(x)=−x2−3x+2f ( x ) = - x ^ { 2 } - 3 x + 2f(x)=−x2−3x+2

Graph the Quadratic Function $f ( x ) = - x ^ { 2 } - 3 x + 2$