Answer:
The vertex of the function is at (1,-25)
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one.
Part of the graph of the function f(x) = (x + 4)(x-6) is shown below.
Which statements about the function are true? Select two
options.
The vertex of the function is at (1,-25).
The vertex of the function is at (1,-24).
The graph is increasing only on the interval -4< x < 6.
The graph is positive only on one interval, where x <-4.
The graph is negative on the entire interval
My answer:
Given the factored form of the function:
f(x) = (x + 4)(x-6)
<=> f(x) = [tex]x^{2} - 2x -24[/tex]
We will convert to vertex form
<=> f(x) = ([tex]x^{2} - 2x +1[/tex]) - 25
<=> f(x) = [tex](x-1)^{2} -25[/tex]
=> the vertex of the function is: (1,-25)
We choose: a. The vertex of the function is at (1,-25)
Let analyse other possible answers:
c. The graph is increasing only on the interval -4< x < 6.
Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.
So the graph is increasing in the domain (1, +∞)
=> C is wrong
d. The graph is positive only on one interval, where x <-4
Wrong, The graph is positive only on one interval, where x > 6
e. The graph is negative on the entire interval
Wrong, The graph is negative only on one interval, where -4< x < 6.
