Question

A parabola has the equation f(x) = 2(x − 3)2 − 4. Complete:

1. The vertex is ____________. 2. The graph opens _________________. 3. The function has a minimum value of _____________________.

Answer 1

see explanation

Explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 2(x - 3)² - 4 ← is in vertex form

with (h, k) = (3, - 4), thus

1 the vertex is (3, - 4 )

Consider the value of a

• If a > 0 then graph opens up and is a minimum

• If a < 0 then graph opens down and is a maximum

2 Here a = 2 thus the graph opens up

The max/ min value of the function is the y- coordinate of the vertex, thus

3 The function has a minimum value of - 4