Question

Determine if the following function can be used to model the graph

if yes, write two reasons why
if no, write one reason why not
f(x)= -5(x+6)² + 2

Answer 1

To determine if f(x) = -5(x+6)² + 2 can model a graph, the graph must be a downward opening parabola with the vertex at (-6, 2). If the graph's shape and vertex do not match, the function is not suitable.

Step-by-step explanation:

The question seeks to establish whether the function f(x) = -5(x+6)² + 2 can model a specific graph. Without seeing the graph, one can assert that this function represents a downward opening parabola with a vertex at (-6, 2). This function cannot model a horizontal line or a graph that has an upwards trend, a y-intercept that does not match the given function, or data that is not along a parabolic curve.

To determine if this function is the correct model, we need to check two things:

• The shape of the graph: If the graph is a parabola that opens downwards.
• The vertex of the graph: If the graph's highest point is at (-6, 2).

If the graph does not meet these conditions, then f(x) = -5(x+6)² + 2 is not a suitable model. For example, if the graph is a horizontal line, a line with a positive slope, or any shape other than a downward-opening parabola, then the given function would not be able to model it correctly.