Respuesta :
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).
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:
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