I need help!!!! Find the minimum or maximum y-value for f(x) = 3x^2 + 12x + 4.

Question

Find the minimum or maximum y-value for f(x) = 3x^2 + 12x + 4. Tell me whether it is a minimum (MIN) or maximum (MAX), then type a comma, then tell me the value. For example, if you find a minimum value of -40, you would type: MIN,-40

Answer 1

Hi Caleb, for the function f(x) = 3x² + 12x + 4, we need to find the vertex. The vertex is found by first finding x, and then substituting for x in the function.

 

Finding x:

 

x = - b / 2a, where b is the coefficient of the x term and a is the coefficient of the x² term.

 

x = - 12 / (2 * 3)

 

x = -2

 

Finding y:

 

 To find y, substitute for x in the given function

 

y = 3 * (-2)² + 12 * (-2) + 4

 

y = 12 - 24 + 4

 

y = -16

 

Vertex:

 

The vertex is (-2, -16)

 

Since the coefficient of the x² term is positive, we have a minimum.

 

The minimum is at -16.

 

Your answer:

 

MIN,-16

 

Questions?