Question

1. What is the vertex of f(x) = 3(x + 2)^2 - 4?

2. Does this function have a maximum or minimum value? f(x) = (x - 4)^2 +3?

Answer 1

• 3) A. (-2, - 4);
• 4) B. Minimum.

----------------------------

Question 3

The vertex form of a parabola is:

• f(x) = a(x - h)² + k, where a - leading coefficient, (h, k) - the vertex

Given equation is:

• f(x) = 3(x + 2)² - 4

Hence h = - 2, k = - 4, therefore its vertex is (- 2, - 4).

Question 4

• When a > 0, the graph opens up, it means the function has a minimum but no maximum value;

• When a < 0, the graph opens down, it means the function has a maximum but no minimum value.

Given function:

• f(x) = (x - 4)² + 3,

It has a = 1, hence the graph opens up, therefore the function has a minimum.