Question

Which of the following is the graph of f(x) = x2 − 4x − 5?

A. graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5

B. graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C. graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D. graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4

Answer 1

The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)

Answer 2

Minimum at (2,-9) and intercepts are (-1,5)

Explanation:

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

completing square method adding and subtracting the square of half of coefficient of 4 ,we get

f(x) =
`x^2 -4x+4 -4 -5`

f(x) =
`(x-2)^2 -9`

on comparing it with standard vertex form
`(x-h)^(2) +k`

where k is suppose to be the minimum value

on comparing it we get k = -9

which is minimum value of f(x)

at x =2

and if we find the zeros of

`x^2 -4x-5` ,we get

`x^2 -5x+x -5`

`x^2 -4x-5`

x(x-5)+1(x-5)

(x+1)(x-5)

on setting it equals zero ,we get

x+1 =0 and x=5

x =-1 and x=5

therefore option A is answer

Minimum at (2,-9) and intercepts are (-1,5)