Given the function ƒ(x) = x 2 - 4x - 5 identify the zeros using factorization. draw a graph of the function. its vertex is at (2, -9).

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

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

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

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.

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:

, with the symmetry axis

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

1. There are 3 ways to solve quadratic equations

We use the factoring method

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

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)

domain of the function

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the inverse of the ƒunction  

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

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Keywords : Quadratic function, vertex,graph

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step-by-step explanation: