Question

Part of the graph of the function f(x) = (x - 1)(x + 7) is

shown below.
Which statements about the function are true? Select
three options.
The vertex of the function is at (-4,-15).
6
The vertex of the function is at (-3,-16).
4
The graph is increasing on the interval x > -3.
2
The graph is positive only on the intervals where x <-7
and where
X > 1.
+
-8
-6
-4
-2
2
х
2.
The graph is negative on the interval x < -4.
4
-6
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Answer 1

THE CORRECT ANSWERS ARE 2,3,4!

Explanation:

TOOK THE TEST ON EDGE

Answer 2

Explanation:

The given function is

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

Zeroes of the function are

`(x-1)(x+7)=0`

`x=-7,1`

It means, f(x) intersect x-axis at x=-7 and x=1.

Mid value of -7 and 1 is the x-coordinate of the vertex.

`(-7+1)/(2)=-3`

At x=-3,

`f(-3)=(-3-1)(-3+7)=(-4)(4)=-16`

So, the vertex of the function is at (-3,-16).

The given function can be written as

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

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

Here leading coefficient is negative, it means it is an upward parabola.

So, we conclude that

1. The graph is increasing on the interval x > -3.

2. The graph is decreasing on the interval x < -3.

3. The graph is positive only on the intervals where x <-7 and where x > 1.

4. The graph is negative only on the intervals where -7 < x < 1.

Therefore, the correct options are 2, 3 and 4.