Exercise 10 Page 965

We are asked to write an equation for the parabola that has its axis of symmetry at $x=\text{-}3.$ Also, we know that its range includes all real numbers less than or equal to $4.$ This means that the parabola faces downward and its absolute maximum point goes to $4.$ Let's see its graph!

As we can see from the graph, the vertex of this parabola lies at $(\text{-}3,4).$ By knowing these, we can use the Vertex Form of a quadratic function to write our equation. Let's remember it! In this form $a$ gives the direction of the parabola. When $a>0$ the parabola faces upward and when $a<0$ it faces downward. Moreover, $(h,k)$ represents the vertex of the parabola. Knowing this, let's substitute $h=\text{-}3$ and $k=4$ into the above equation. Great! Now, we can eliminate the options F and G because they have different vertices. Next, let's consider the value of $a.$ Since we know that our function opens downward, the value of $a$ must be negative. Therefore, we can conclude that our only possible answer would be option H in the case of $a=\text{-}1.$