Question

1. find the vertex.

$y = 3x^2 - 12x + 6$
$(2, 3)$
$(2, -6)$
$(3, 6)$
$(6, 2)$

1. choose the best answer.

a ___ is the intersection of a plane with one or both nappes of a double cone.
nappe
double cone
conic section
cone

Explanation:

For Question 9:

Step1: Find x-coordinate of vertex

For quadratic $y=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=3$, $b=-12$.
$x=-\frac{-12}{2\times3}=\frac{12}{6}=2$

Step2: Find y-coordinate of vertex

Substitute $x=2$ into $y=3x^2-12x+6$.
$y=3(2)^2-12(2)+6=3\times4-24+6=12-24+6=-6$

This is a definition-based question. A conic section is specifically defined as the shape formed when a plane intersects one or both parts (nappes) of a double cone. The other terms refer to the components of this system, not the resulting intersection.

Answer:

(2, -6)

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For Question 10: