Question

graph the function f(x) = x² - 6x - 1.
plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10)

Explanation:

Step1: Find vertex x-coordinate

For $f(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=1, b=-6$:
$x = -\frac{-6}{2(1)} = 3$

Step2: Find vertex y-coordinate

Substitute $x=3$ into $f(x)$:
$f(3) = 3^2 - 6(3) - 1 = 9 - 18 - 1 = -10$

Step3: Find a second point

Choose $x=0$, substitute into $f(x)$:
$f(0) = 0^2 - 6(0) - 1 = -1$

Answer:

1. Vertex point: $(3, -10)$
2. Second point: $(0, -1)$

(Plot these two points and draw a symmetric parabola opening upwards through them.)