Select all the statements about functions g(x) = x2 − 4x + 3 and f(x) = x2 − 4x that are true. 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. D. The graphs never intersect. E. The graphs have the same y-intercept.

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  A, B, D

Step-by-step explanation:

We observe that g(x) = f(x) +3, which means it is the graph of f(x) translated up 3 units. That translation does not change the axis of symmetry, but it puts the vertex of g above the vertex of f (by 3 units).

Since each point on the graph of g is 3 units above the corresponding point of f, the graphs cannot intersect.

The true statements are ...

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.

D. The graphs never intersect.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.