1. graph the following equations using bert method:\n(a) ( y = - 2 ( x + 6 ) ^ { 2 } - 2 )\n(b) ( y = 1 / 2…

Explanation:

Step1: Identify the vertex form of a parabola

The vertex form of a parabola is (y = a(x - h)^{2}+k), where ((h,k)) is the vertex. For the equation (y=-2(x + 6)^{2}-2), we can rewrite it as (y=-2(x-(-6))^{2}+(-2)). So, (h=-6) and (k = - 2), and the vertex is ((-6,-2)).

Step2: Determine the direction of the parabola

Since (a=-2<0), the parabola opens downwards.

Step3: Find some additional points

Let's choose (x=-5): [ \begin{align*} y&=-2(-5 + 6)^{2}-2\ &=-2(1)^{2}-2\ &=-2-2\ &=-4 \end{align*} ] Let's choose (x=-7): [ \begin{align*} y&=-2(-7 + 6)^{2}-2\ &=-2(-1)^{2}-2\ &=-2-2\ &=-4 \end{align*} ] Let's choose (x=-4): [ \begin{align*} y&=-2(-4 + 6)^{2}-2\ &=-2(2)^{2}-2\ &=-8-2\ &=-10 \end{align*} ] Let's choose (x=-8): [ \begin{align*} y&=-2(-8 + 6)^{2}-2\ &=-2(-2)^{2}-2\ &=-8-2\ &=-10 \end{align*} ]

Answer:

Plot the vertex ((-6,-2)). Then plot the points ((-5,-4)), ((-7,-4)), ((-4,-10)), ((-8,-10)) and draw a smooth curve passing through these points (a downward - opening parabola).