Question

What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola `g(x) = 3x^2 + 12x + 15`?

Answer 1

g(x)= 3(x^2 +4x) +15

= 3 (x^2+4x+4-4) +15

= 3(x^2+4x+4) +3

= 3 (x+2)^2 +3

This equation represents a vertical parabola, opening upwards. Vertex is (-2,3), Axis of symmetry is x= -2. Minimum value is 3, maximum is infinity.Range is [3, inf)