Short Answer 
The quadratic function is expressed as y = ax² + bx + c, with its graph being a parabola that opens upwards if a > 0 and downwards if a < 0. For the function y = x² - 4, the vertex is at (0, -4) and it intersects the x-axis at (-2, 0) and (2, 0). The correct graph representation includes an upward-opening parabola intersecting with a linear equation at the specified points.
Step 1: Understand the Quadratic Function
A quadratic function takes the form of y = ax¬¨‚⧠+ bx + c, where “a”, “b”, and “c” are constants. The shape of the graph of a quadratic function is always a parabola, which can either open upwards or downwards depending on the sign of “a”. If a > 0, the parabola opens upwards, while if a < 0, it opens downwards.
Step 2: Analyze the Given Equations
For the quadratic function y = x¬≤ Р4, we can identify the vertex of the parabola and its behavior. The vertex of this specific function is at the point (0, -4). Additionally, the points where the parabola intersects the x-axis (also known as the roots) can be found at (-2, 0) and (2, 0), indicating its symmetry about the y-axis.
Step 3: Identify the Graph Representation
The correct graph for the system of equations consisting of y = x¬≤ Р4 and x + y + 2 = 0 is the one that shows an upward parabola and a linear equation. The line will intersect at points (-2, 0) and (0, -2). Thus, when analyzing graphs, look for a parabolic curve opening upwards with the aforementioned characteristics to confirm the correct graph representation.