Question

Consider the quadratic function f(x)=x^2+3x+2 and (a) find the vertex; (b) find the axis of symmetry; (c) determines whether there is a maximum or a minimum value, and find that value; and (d) graph the function

Answer 1

a) f(x) = x^2 + 3x + 2

f'(x) = 2x + 3 = 0

x = -1.5

b) obviously, the axis of symmetry will pass through the vertex, so the axis of symmetry is described by the equation x = -1.5

c) minimum is reached at the vertex, because f'(0) > 0 and f'(-2) < 0.

minimum value is f(-1.5) = -0.25.

the function has no more extremum points, which means there is no maximum

d)