Linear-Quadraric Systems of Equations: Matching equations to graphs

To solve this problem, we need to determine whether the provided graph corresponds to a quadratic or linear function.

• First, we observe the shape of the graph.
• The graph shows a downward curve, indicating it is a parabola.
• The general form of a quadratic equation $(y = ax^2 + bx + c)$ implies graph types.
• Let's verify if one of the given quadratic choices represents this graph.

Since the graph is a parabola opening upwards, we'll evaluate the given quadratic equation $y = x^2 - 6x + 8$. Analyzing it and comparing leads to:

• The vertex form can be rewritten or identified mathematically or visually from the given expression.
• This quadratic formula aligns with prominent features of the parabola: its vertex, orientation, and intercepts, matching the graph.

Thus, as the parabola aligns perfectly with quadratic properties such as opening upwards, the formula that describes graph 1 correctly is:
$y = x^2 - 6x + 8$.