Question

Functions f(x) and g(x) are shown below:


f(x) g(x)
f(x) = 3x2 + 12x + 16 g(x) = 2 sin(2x - π) + 4


Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.

Answer 1

the minimum of a parabola is at the "vertex"
can you find the x value of the vertex ?

Answer 2

i dont know

Answer 3

find the derivative and equate it to zero............the derivative of a function at minimum and maximum values are zero

Answer 4

see http://hotmath.com/hotmath_help/topics/vertex-of-a-parabola.html
see the example

Answer 5

is the vertex 12

Answer 6

@phi

Answer 7

did you find the formula to find the vertex at the site I posted?

Answer 8

y = ax2 + bx + c.

Answer 9

you need to know that. But you also need a formula for the vertex.
Look for the sentence right above the Example box.

Answer 10

y = ax2 + bx + c.

Answer 11

@phi

Answer 12

This site gives it step by step
http://www.wikihow.com/Find-the-Vertex-of-a-Quadratic-Equation

Answer 13

@phi how do find the minim est value of the functiooons.

Answer 14

first find the x value of the vertex of the parabola. x = -b / (2a)
use that x value in the equation of the parabola to find the y value (this will be the min value you need)

Answer 15

whats the -b and a value that i plug in @phi

Answer 16

you should match these equations
\[ f(x) = ax^2 + \ b\ x +\ c \\ f(x)=3x^2 + 12x + 16\]
do you see the pattern?

Answer 17

@phi