graph the function f(x) = -3x². plot the vertex. then plot another point on the parabola. if you make a…

Explanation:

Step1: Identify the vertex form of a parabola

The general form of a parabola is $y = ax^{2}+bx + c$. For the function $f(x)=-3x^{2}$, we have $a=-3$, $b = 0$, $c = 0$. The x - coordinate of the vertex of a parabola $y=ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $b = 0$ and $a=-3$ into the formula, we get $x = 0$. To find the y - coordinate of the vertex, we substitute $x = 0$ into the function $f(x)=-3x^{2}$. So $f(0)=-3\times0^{2}=0$. The vertex is $(0,0)$.

Step2: Find another point on the parabola

Let's choose $x = 1$. Substitute $x = 1$ into the function $f(x)=-3x^{2}$. Then $f(1)=-3\times1^{2}=-3$. So another point on the parabola is $(1, - 3)$.

To graph: Plot the vertex $(0,0)$ on the coordinate - plane. Then plot the point $(1,-3)$. Since the parabola $y=-3x^{2}$ is symmetric about the y - axis, the point $(-1,-3)$ is also on the parabola. Draw a smooth curve passing through these points.

Answer:

Vertex: $(0,0)$; Another point: $(1,-3)$ (and also $(-1,-3)$)