The document is a math project on the quadratic formula. It defines the quadratic formula as the formula that provides solutions to quadratic equations. It then derives the quadratic formula step-by-step, showing how it is obtained by rearranging the standard form quadratic equation. Finally, it provides 3 examples of solving quadratic equations using the quadratic formula.

1. Math Project
Mahrukh Shehzadi
BSBB-F19-028
Topic: Quadratic formula
SubmissionTo: Sir Sajawal Naeem

2. ProjectTopic
Quadratic formula

3. Quadratic Formula
010
Definition:
Quadratic formula is the formula that provides solution to
the quadratic equation.There a re also other methods to
solve the quadratic equation. Quadratic formula can also be
use to indicate the axis of symmetry of the parabola.And
the number of real zeros the quadratic equation contains.

5. Derivation of Quadratic Formula
❑ The quadratic formula is actually derived using the following
steps:

6.  Step 1. Let
And where a, b and c are real numbers but
 Step 2. Subtract both sides by c and arrange the equation.
Step 3. Divide the whole equation by co-efficient of squared term
..

7. Step 4. Identify the co-efficient of linear term
Step 5. Now square and divide the term
Step 6. Add the result of previous step at both sides of equation.

8.  Step 7. Now simplify the equation.
 Step 8. Express trinomial as square of binomial

9.  Step 9. Take square of the both sides of equation.
 =
Step 10. Apply sign in the equation
Step 11. Keep variable x apart.
=

10.  Step 12. Now, simplify and derive.
 Hence, the quadratic formula has derived.
.
Step 12. Now, simplify and derive

11. Examples
 Question No.1
Solve the following examples by using quadratic formula.
Solution:
Now arranging the equation:
Now,

12.  According to the quadratic formula:
=
=
=
=
=
=
=

14. Question No.2
 Solve the following question by quadratic formula:
 Solution:
Let;
By using quadratic formula:
=

17. Question No.3
 ;
Solve the following question:
Solution:
Simplify and write equation in standard form:

18. Or
As quadratic formula is:

19.  OR
 Hence the answer is -8 and-1