Answer: To match the given equations with their corresponding graphs, let's analyze each equation and graph:
1. f(x) = x² + 2x - 5:
This is a quadratic equation in standard form with a positive coefficient for the x² term. The graph of this equation will be a parabola opening upward. It will have a vertex and may intersect the x-axis at two points.
2. f(x) = x² - 2x + 3:
This is a quadratic equation in standard form with a positive coefficient for the x² term. The graph of this equation will be a parabola opening upward. It will have a vertex and may not intersect the x-axis (no real roots).
3. f(x) = x² - 6x + 8:
This is a quadratic equation in standard form with a positive coefficient for the x² term. The graph of this equation will be a parabola opening upward. It will have a vertex and may intersect the x-axis at two points.
4. f(x) = 4x² - 16:
This is a quadratic equation in standard form with a positive coefficient for the x² term. The graph of this equation will be a parabola opening upward. It will have a vertex and may intersect the x-axis at two points.
Now, let's match the equations with their corresponding graphs:
Graph A: f(x) = x² + 2x - 5
Graph B: f(x) = x² - 2x + 3
Graph C: f(x) = x² - 6x + 8
Graph D: f(x) = 4x² - 16
Please note that without visual representations of the graphs or additional information, I cannot provide an exact matching. However, based on the characteristics of the equations, you can use the descriptions provided above to match them with the respective graphs.
Step-by-step explanation: Hope this helps!!!