Solve quadratic equations using the quadratic formula
Use the discriminant to predict the number of solutions of a quadratic equation
Identify the most appropriate method to use to solve a quadratic equation
Before you get started, take this readiness quiz.
Simplify:
.
If you missed this problem, review
[link] .
Simplify:
.
If you missed this problem, review
[link] .
Simplify:
.
If you missed this problem, review
[link] .
When we solved quadratic equations in the last section by completing the square, we took the same steps every time. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes.’ In this section, we will derive and use a formula to find the solution of a quadratic equation.
We have already seen how to solve a formula for a specific variable ‘in general’ so that we would do the algebraic steps only once and then use the new formula to find the value of the specific variable. Now, we will go through the steps of completing the square in general to solve a quadratic equation for
x . It may be helpful to look at one of the examples at the end of the last section where we solved an equation of the form
as you read through the algebraic steps below, so you see them with numbers as well as ‘in general.’
This last equation is the Quadratic Formula.
Quadratic formula
The solutions to a quadratic equation of the form
,
are given by the formula:
To use the Quadratic Formula, we substitute the values of
into the expression on the right side of the formula. Then, we do all the math to simplify the expression. The result gives the solution(s) to the quadratic equation.
How to solve a quadratic equation using the quadratic formula
Solve a quadratic equation using the quadratic formula.
Write the Quadratic Formula in standard form. Identify the
,
, and
values.
Write the Quadratic Formula. Then substitute in the values of
,
, and
Simplify.
Check the solutions.
If you say the formula as you write it in each problem, you’ll have it memorized in no time. And remember, the Quadratic Formula is an equation. Be sure you start with ‘
’.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life