Question

Given the function ƒ(x) = x 2 - 4x - 5

Answer 1

The function ƒ (x) = x² - 4x - 5  using factorization.: (x-5) (x+1)

The intersection point (5,0), (-1,0) and (0,-5)

Further explanation

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

$\large{\boxed{\bold{f(x)=ax^2+bx+c}}}$

where a, b, and c are real numbers and a ≠ 0.

The parabolic curve can be opened up or down determined from the value of a.

• If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value

The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.

Steps to draw a graph of quadratic functions:

• 1. Determine the point of intersection with the x-axis (y = f (x) =0)
• 2. Determine the point of intersection with the y axis (x = 0).
• 3. Determine the maximum / minimum point of the quadratic function

$(- \frac {b} {2a}, - \frac {b ^ {2} - 4ac} {4a})$, with the symmetry axis

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

Solution for the function ƒ (x) = x² - 4x - 5

1. There are 3 ways to solve quadratic equations

• a. factoring b. perfect squared c. quadratic formula

We use the factoring method

 Quadratic equation x²+ bx+c = 0 is equivalent to  quadratic equation

${\displaystyle {x^2+(p+q)\times\:pq}}$

where p+q = b and px q = c

for a = 1, the result of factoring is (x+p) (x+q)

So the equation x² - 4x - 5

p+ q = -4 and p x q = -5,

can be factored into

(x-5) (x+1)

We draw the graph:

1. the intersection of the x-axis (y = 0)

(x-5) = 0 ---> x = 5, the intersection point (5,0)

(x +1) = 0 ---> x = -1, the intersection point (-1,0)

2. the intersection of the y axis (x = 0) ---> y = -5

3. the peak point(vertex) is known: (2, -9)

Learn more  

domain of the function

brainly.com/question/4135536

the inverse of the ƒunction  

brainly.com/question/9289171  

F (x) = x2 + 1 g (x) = 5 - x

htps://brainly.com/question/2723982

Keywords : Quadratic function, vertex,graph

Answer 2

Answer:

The zeroes of the function f(x) are -1 and 5.

Step-by-step explanation:

The given function is

$f(x)=x^2-4x-5$

The middle term can be written as -5x+x.

$f(x)=x^2-5x+x-5$

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

Taking out common factors.

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

Equate the given function equal to 0, to get the zeroes.

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

Using zero product property,

$x-5=0\Rightarrow x=5$

$x+1=0\Rightarrow x=-1$

Therefore the zeroes of the function f(x) are -1 and 5.

The vertex of the function is at (2,-9) and the x-intercepts are at (-1,0) and (5,0). So the graph of given function is shown below.