64 POINTS

Write your own quadratic equation in standard form. Convert this quadratic to factored form. Be sure to show all of your work. Post the two equations and the work you did to convert from quadratic form to standard form. Now write a new, different quadratic function, f of x, in standard form. Convert this quadratic function to factored form. Post to the discussion board both of these functions and the work you completed to convert from the quadratic form of the function to the factored form of the function. Use your factored equation and your factored function to explain the differences between roots, x-intercepts, zeros, and solutions.

Refer below for detailed explanation.

Step-by-step explanation:

Standard equation:

1. ax^2+bx+c=0.

Quadratic formula:

2. x = -b+-sqrt(b^2-4ac)/2a. .

Now two equations to find the factored form through these formulas above.

Through this identifying a,b and c.

ax^2+bx+c=0.

x^2+4x-21=0

Here a=1, b=4, and c= -21

Now applying in the quadratic formula.

x=-4+-sqrt(4^2-4(1)(-21))/2(1)

Now solve it and it becomes

x=3 or x= -7.

Another example :

x^2+3x-4=0

Here a=1, b=3 and c=-4.

X=-3+-sqrt(3^2-4(1)(-4))/2(1)

Now solve it and

x= -4 and x=1

P.s have attached the picture of quadratic formula as well.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get