Question

Two quadratic functions are shown.

Function 1:

f(x) = 3x2 + 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)

Answer 1

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

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)