The problem involves solving the system of equations by graphing, as shown in the uploaded image:

1. $y = -2x - 3$ (a linear equation)
2. $y = (x + 3)^2 + 4$ (a quadratic equation)

Step-by-Step Solution:

1. Graph the Linear Equation $y = -2x - 3$:

   • This is a straight line with slope $-2$ and y-intercept $-3$.
   • Two points on this line are:
     • At $x = 0$, $y = -3$.
     • At $x = 1$, $y = -5$.
   • Plot these points and draw the straight line passing through them.

2. Graph the Quadratic Equation $y = (x + 3)^2 + 4$:

   • This is a parabola with its vertex at $(-3, 4)$.
   • At $x = -2$ and $x = -4$, $y = 5$ (symmetric points around the vertex).
   • At $x = -1$ and $x = -5$, $y = 8$.
   • Plot these points and draw the parabola.

3. Find Intersection Points:

   • The graph shows the two curves intersecting at approximately:
     • $x = -4$, $y = 6$
     • $x = -1.5$, $y = 0$

These intersection points represent the solutions to the system of equations.

Solutions:

The solutions are:

• $(-4, 6)$
• $(-1.5, 0)$

Would you like a detailed explanation of graphing, intersections, or solving algebraically?

Related Questions:

1. How do you find the intersection of two equations algebraically?
2. What are some tips for identifying the vertex of a parabola?
3. How does the slope of a line affect its steepness and direction?
4. How can symmetry help when plotting a parabola?
5. What are alternative methods for solving systems of equations (besides graphing)?

Tip:

When graphing systems of equations, always verify intersection points by substituting them back into both equations.