Question

WILL GIVE BRAINLIEST Use the function f(x) = x^2 - 6x + 3 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). 3 6 12 18

Answer 1

Answer:

18

Step-by-step explanation:

To find the minimum value of the function we have to find the vertex.

$f(x) = x^2 - 6x + 3$

Vertex point is $(h, k)$

$h=\frac{-b}{2a}$

$h=\frac{-(-6)}{2(1)}$

$h=\frac{6}{2}$

$h=3$

In order to find $k$

$f(h) = h^2 - 6h + 3$

$k=f(3) = 3^2 - 6(3) + 3$

$k= 9 - 18 + 3$

$k=-6$

Vertex point is $(3, -6)$

The difference between the maximum value of $g(x)$ and the minimum value of $f(x)$ is

$12-(-6)=12+6=18$

Answer 2

To find the max/ min of a function use the formula x = - b/2a

in the function x^2 - 6x +3, a would be the number in front of the x^2, since there is no number, a = 1. b is the number in front of x , which is -6, so b = -6

Now you have x = -(-6) /2(1) = 6/2 = 3

Now you have a value for x, replace it in the formula and solve:

3^2 - 6(3) + 3 = 9 -18 +3 = -6

The minimum is -6

The max of the graph is the highest point which is 12

The difference is 12 - -6 = 12 +6 = 18

The answer is 18