Question

Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value. G(x) = 2 sin (x-π) F(x) = 3x^2 + 12x + 16

Answer 1

G(x): no matter what x is, the minimum of sin is -1, so G(x) has a minimus of 2*(-1), which is -2
to find the minimum of F(x), it is a quadratic equation, the minimum or maximum is when x=-b/(2a). In this case, a=3, b=12, so x=-2
Plug x=-2 into the equation, you will get F(x)=4, so the minimum y value is 4

Note: when a is positive, the parabola opens upward, the function has a minimum y value. when a is negative, the parabola opens downward, the function has a maximum value