The graph of a quadratic function has x-intercepts of -7and -1 ,and passes through the point (-4,36). determine the equation of the quadratic function in the form f(x)=a(x-m)(x-n)

Step-by-step explanation:

Quadratic equation:

A quadratic equation, with roots(x-intercepts) at and , and leading coefficient a, is given by:

Has x-intercepts of -7 and -1

So . Thus

Passes through the point (-4,36).

This means that when , and we use this to find the leading coefficient.

So

step-by-step explanation:

f

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: