The true statements about g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are
The functions are given as:
[tex]g(x) = x^2 - 4x + 3[/tex]
[tex]f(x) =x^2 - 4x[/tex]
Start by differentiating the function g(x)
g'(x) = 2x - 4
Set to 0
2x - 4 = 0
Add 4 to both sides
2x = 4
Divide by 2
x = 2 ----- this represents the axis of symmetry of function g(x)
Substitute x = 2 in [tex]g(x) = x^2 - 4x + 3[/tex]
[tex]g(2) = 2^2 -4*2 + 3[/tex]
g(2) = -1
This means that the vertex of the function g(x) is (2,-1)
Next, differentiate the function f(x)
f'(x) = 2x - 4
Set to 0
2x - 4 = 0
Add 4 to both sides
2x = 4
Divide by 2
x = 2 ----- this represents the axis of symmetry of function f(x) (same as g(x))
Substitute x = 2 in [tex]f(x) =x^2 - 4x[/tex]
[tex]f(2) = 2^2 -4 * 2[/tex]
f(2) = -4
This means that the vertex of the function f(x) is (2,-4)
By comparing the vertices (2,-4) and (2,-1).
We can see that (2,-4) is below (2,-1).
Hence, the true statements are (a) and (b)
Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select all that apply.
A. The vertex of the graph of function g is above the vertex of the graph of function f.
B. The graphs have the same axis of symmetry.
c. Function f has a maximum value and function g has a minimum value.
Read more about quadratic functions at:
https://brainly.com/question/16041497
#SPJ1
