Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply. The function in vertex form is f(x) = (x – 4)2 – 11. The vertex of the function is (–8, 5). The axis of symmetry is x = 5. The y-intercept of the function is (0, 5). The function crosses the x-axis twice.

QUESTION POSTED AT 01/06/2020 - 02:50 PM

Answered by admin AT 01/06/2020 - 02:50 PM

Answer:

Step-by-step explanation:

Using "completing the square," write f(x) = x^2 – 8x + 5 in vertex form.  Note:  Use " ^ " to denote exponentiation.

f(x) = x^2 – 8x + 5 = x^2 - 8x + 16 - 16 + 5, or

1)  f(x) =                        (x -4)^2 - 11  This is the function in vertex form.  (TRUE)

2)  The axis of symmetry is x = 4, not x = 5.  (FALSE)

3) The y-intercept of this function is (0, 5) (TRUE)

4)  The function crosses the x-axis twice.

     From the vertex form, (x -4)^2 - 11 , we see that the vertex is at (4, - 11), which is below the x-axis.  Since the parabolic graph opens up, the graph does cross the x-axis twice.  (TRUE)

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