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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

WILL GIVE BRAINLIEST Use the function fx x2 6x 3 and the graph of gx to determine the difference between the maximum value of gx and the minimum value of fx 3 6 class=

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musiclover10045

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

mirai123

Answer:

18

Step-by-step explanation:

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

[tex]f(x) = x^2 - 6x + 3[/tex]

Vertex point is [tex](h, k)[/tex]

[tex]$h=\frac{-b}{2a} $[/tex]

[tex]$h=\frac{-(-6)}{2(1)} $[/tex]

[tex]$h=\frac{6}{2} $[/tex]

[tex]h=3[/tex]

In order to find [tex]k[/tex]

[tex]f(h) = h^2 - 6h + 3[/tex]

[tex]k=f(3) = 3^2 - 6(3) + 3[/tex]

[tex]k= 9 - 18 + 3[/tex]

[tex]k=-6[/tex]

Vertex point is [tex](3, -6)[/tex]

The difference between the maximum value of [tex]g(x)[/tex] and the minimum value of [tex]f(x)[/tex] is

[tex]12-(-6)=12+6=18[/tex]