Question

Explain why the graph of the equation g(x) = -(x + 1 ) - 3 would be a parabola opening downward.

Answer 1

Answer: Because the a-value is negative.

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

• "a" is the vertical stretch
• -a is a reflection over the x-axis
• h is the horizontal shift (positive = right, negative = left)
• k is the vertical shift (positive = up, negative = down)

Given: g(x) = - (x + 1)² - 3

                    ↓

                 a= -1

Since the a-value is negative, the parabola will be reflected over the x-axis which will change the curve from (U-shaped) to (∩-shaped).