Question

Please help me out!​

Answer 1

Answer:

Second option

Third option

Fourth option

Step-by-step explanation:

We have the following quadratic function

$f(x) =(x-1)(x+7)$

Use the distributive property to multiply the expression

$f(x) =x^2+7x-x-7$

$f(x) =x^2+6x-7$

For a function of the form $f (x) = ax ^ 2 + bx + c$ the x coordinate of the vertex is:

$x =-\frac{b}{2a}$

Then in this case the coordinate of the vertex is:

$x =-\frac{6}{2(1)}$

$x =-3$

To obtain the y coordinate of the vertex we evaluate the function at $x = -3$

$f(-3) =(-3)^2+6(-3)-7$

$f(-3) =9-18-7$

$f(-3) =-16$

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 $x$ and $x> 1$

The correct answers are:

Second option

Third option

Fourth option