which statements about functions g(x)=x2-4x+3 and f(x)=x2-4x are true. select all that apply.
1.the vertex of the graph of function g is above the graph of function f.
2. the graphs have the same axis of symmetry.
3. function f has a maximum value and function g has a minimum value.
Answers
Given : g(x)=x²-4x+3
f(x) = x² - 4x
To find : which statements about functions are true.
1.the vertex of the graph of function g is above the graph of function f.
2. the graphs have the same axis of symmetry.
3. function f has a maximum value and function g has a minimum value.
Solution:
g(x)=x²-4x+3
=> g(x) = (x - 3)(x - 1)
Zeroes = 3 and 1
Axis of symmetry = (3 + 1)/2 = 2
g'(x) = 2x - 4
x = 2
g''(x) = 2 hence minimum at x = 2
g(2) = 2² - 4(2) + 3 = - 1
Vertex ( 2 , -1)
f(x) = x² - 4x
=> f(x) = x(x - 4)
Zeroes are 0 , 4
Axis of symmetry = (0 + 4)/2 = 2
f'(x) = 2x - 4
=> x = 2
f''(x) = 2 hence minimum at x = 2
f(2) = 2² - 4(2) = - 4
Vertex ( 2 , - 4)
.the vertex of the graph of function g is above the graph of function f. TRUE
as - 1 > - 4
the graphs have the same axis of symmetry. TRUE
axis of symmetry x = 2
function f has a maximum value and function g has a minimum value. - FALSE as both has minimum value
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