Answer:
Second option
Third option
Fourth option
Step-by-step explanation:
We have the following quadratic function
[tex]f(x) =(x-1)(x+7)[/tex]
Use the distributive property to multiply the expression
[tex]f(x) =x^2+7x-x-7[/tex]
[tex]f(x) =x^2+6x-7[/tex]
For a function of the form [tex]f (x) = ax ^ 2 + bx + c[/tex] the x coordinate of the vertex is:
[tex]x =-\frac{b}{2a}[/tex]
Then in this case the coordinate of the vertex is:
[tex]x =-\frac{6}{2(1)}[/tex]
[tex]x =-3[/tex]
To obtain the y coordinate of the vertex we evaluate the function at [tex]x = -3[/tex]
[tex]f(-3) =(-3)^2+6(-3)-7[/tex]
[tex]f(-3) =9-18-7[/tex]
[tex]f(-3) =-16[/tex]
Then the vertex is: (-3, -16)
We can see in the graph that the zeros of the function are x=1 and x=-7
Then the function is decreasing from -∞ to -3 and then it is increasing from -3 to ∞
The function is positive for [tex]x <-7[/tex] and [tex]x> 1[/tex]
The correct answers are:
Second option
Third option
Fourth option
