Consider the graph at right as you answer the following questions. Homework Help ✎

1. What is the equation of the parabola?

   Hint (a):

   Use the vertex to help you write an equation in graphing form.

   More Help (a):

   vertex: $(−3,−2)$
   $y=a(x−h)^2+k$

2. What is the equation of the line?

3. Use the graph to solve $x+5=\frac{1}{2}(x+3)^2-2$. How can you verify that your solution(s) are correct?

   Answer (c):

   $x=−5$ and $x=1$

4. Use the graph to solve the system below.
   $y=\frac{1}{2}(x+3)^2-2$
   $y=x+5$

   Hint (d):

   Your answers should be in the form $(x,y)$.

5. Use the graph to solve the inequality $x+5<\frac{1}{2}(x+3)^2-2$.

   Answer (e):

   $x<−5$ or $x>1$

6. Use the graph to solve $\frac{1}{2}(x+3)^2-2=0$.

   Answer (f):

   $x=−5$ and $x=−1$

7. How could you change the equation of the parabola so that the parabola and the lines do not intersect? Is there more than one way?

   Hint (g):

   What can you do to the equation of the parabola to change its position on the graph?
   How can you move it up or flip it over?