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
[tex]\large{\boxed{\bold{f(x)=ax^2+bx+c}}}[/tex]
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
[tex](- \frac {b} {2a}, - \frac {b ^ {2} - 4ac} {4a})[/tex], with the symmetry axis
[tex]x = - \frac {b} {2a}.[/tex]
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
[tex]{\displaystyle {x^2+(p+q)\times\:pq}}[/tex]
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
