Chapter 8.1, Problem 3E

To determine

To state:Identify the characteristics of the quadratic function and its graph

Answer to Problem 3E

The given quadratic function is a parabola with vertex at (-1, -1), axis parallel to the y-axis and open downwards. Its equation is given by $y=-{(x+1)}^2-1$ .

Explanation of Solution

Given: The graph of the quadratic is given by

We know that the graph of a quadratic function opens down when it is of the form $y=-f{(x-a)}^2-----(1)$ .

A quadratic graph with vertex at (p, q) which opens down and its axis parallel to the y-axis is of the form $y-q=-{(x-p)}^2=>y=-{(x-p)}^2+q$ which a particular case of (1).

In the given quadratic graph the vertex is at (-1, -1) with its axis is parallel to the y-axis and it opens downwards. Hence the graph must be given by

  $\begin{array}{}$ y=-{(x-(-1))}^2+(-1)$$ =>y=-{(x+1)}^2-1$\end{array}$