Two quadratic functions are shown. Function 1: f(x) = 3×2 + 6x + 7 Function 2:< Question Two quadratic functions are shown. Function 1: f(x) = 3×2 + 6x + 7 Function 2: x g(x) −2 13 −1 7 0 3 1 7 Which function has the least minimum value and what are its coordinates? (5 points) in progress 0 Math 4 weeks 2021-12-27T13:16:16+00:00 2021-12-27T13:16:16+00:00 1 Answer 0 views 0

## Answers ( )

Answer:the function that has the smaller minimum is g(x), and the cordinates are (0,3)Step-by-step explanation:We have a function for f(x) and a table for g(x)

first, quadratic functions are symmetrical.

This means that if the minimum/maximum is located at x = x0, we will have that:

f(x0 + A) = f(x0 – A)

For any real value of A.

Then when we look at the table, we can see that:

g(-1) = 7

g(0) = 3

g(1) = 7

then the minimum of g(x) must be at x = 0, and we can see that the minimum value of g(x) is 3.

Now let’s analyze f(x).

When we have a quadratic equation of the shape.

y = a*x^2 + b*x + c

the minimum/maximum will be located at:

x = -b/2a

In our function we have:

a = 3

b = 6

then the minimum is at:

X = -6/2*3 = -1

f(-1) = 3*(-1)^2 + 6*-1 + 7 = 3 – 6 + 7 = 3 + 1 = 4

Then the function that has the smaller minimum is g(x), and the cordinates are (0,3)