Question

Graph the function f(x) = (x + 1)(x - 5). Use the drop-
down menus to complete the steps needed to graph the
function.
1. Identify the x-intercepts: (-1,0) and (5,0)
2. Find the midpoint between the intercepts: (2,0)
3. Find the vertex:
4. Find the y-intercept:
5. Plot another point, then draw the graph.

Answer 1

Answer:

3) (2,-9)

4) (0,-5)

5) (1,-8)

Step-by-step explanation:

3)

The vertex will occur between you x-intercepts.

You already found that happens at x=2.

To find the corresponding y-coordinate, replace x in

f(x)=(x+1)(x-5) with 2:

f(2)=(2+1)(2-5)

f(2)=(3)(-3)

f(2)=-9

So the vertex is (2,-9).

4)

The y-intercept is when x=0.

So in f(x)=(x+1)(x-5) replace x with 0:

f(0)=(0+1)(0-5)

f(0)=(1)(-5)

f(0)=-5

So the y-intercept is (0,-5).

5)

To find another point just plug in anything besides any x already used.

We preferably want to use a value of x that will keep us on their grid however far up,down,left, or right their grid goes out. So I'm going to choose something close to the vertex which is at x=2. Let's go with x=1.

So replace x in f(x)=(x+1)(x-5) with x=1:

f(1)=(1+1)(1-5)

f(1)=(2)(-4)

f(1)=-8

So another point to graph is (1,-8).

Answer 2

The x intercept of the given function is 6, The midpoint of the intercepts is (2 , 0), the vertex of the function is (-2 , -9), the y intercept of the function is -5 .

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.

f(x) = (x + 1)(x - 5)

f(x) = x(x - 5) + (x - 5)

f(x) = x² - 5x + x - 5

f(x) = x² - 4x - 5

1) Find the x intercept of the function:

f(x) = 0

(x + 1)(x - 5) = 0

x = -1 and x = 5

The coordinates where f(x) = 0 are (-1 , 0) and (5 , 0)

X intercept = ((5-(-1))² + 0²)^(1/2)

X intercept = 6

2) Find the midpoint of X - intercept:

Midpoint ((x₁ + x₂)/2 , (y₁ + y₂)/2)

Midpoint (( 5 + (-1)) / 2 , (0 +0) / 2)

Midpoint of x-intercept is (2 , 0)

3) Find the vertex:

f(x) = a(x - h)^2 + k (Vertex form of parabola)

where h, k is the vertex of the parabola

f(x) = x² - 4x - 5

f(x) = (x+2)^2 - 9 (rewritten in vertex form)

so h = -2 and k = -9

Hence the vertex of the parabola is (-2 , -9)

4) Find the y intercept

f(x) = x² - 4x - 5

put x = 0 for finding the y-intercept

f(x) = -5

Hence the y intercept is -5.

5) The graph of the function is shown below:

Learn more about functions on:

https://brainly.com/question/17043948

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