Question

The functions f(x) = (x + 5)^2 + 2 and g(x) = -(x − 3)^2−3 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

Answer 1

When the leading coefficient is positive, the graph opens up. It means the vertex is its minimum.

When the leading coefficient is negative, the its vertex is its maximum.

• f(x) - vertex is minimum
• g(x) - vertex is maximum