11th class Math Exercise 4.1| 1st year Mathematics | Chapter 4 Exercise 4.1 Question 9 to 14

Completing the square is a powerful technique used to:
1. Solve quadratic equations
2. Find the vertex form of a quadratic function
3. Graph quadratic functions
It involves rewriting a quadratic expression in the form:
ax^2 + bx + c = (x + d)^2 + e
By doing so, we create a perfect square trinomial, which allows us to easily identify the vertex and roots of the quadratic function.
The steps to complete the square are:
1. Move the constant term to the right-hand side
2. Divide the coefficient of x by 2 and square it
3. Add and subtract the result from step 2 on the left-hand side
4. Factor the perfect square trinomial
Example: Complete the square for x^2 + 6x + 8
x^2 + 6x + 8 = (x + 3)^2 + 8 - 9
= (x + 3)^2 - 1
Now we have the vertex form, which reveals the vertex (h, k) = (-3, -1) and the axis of symmetry x = -3.
Completing the square has many applications in mathematics, physics, and engineering, such as:
1. Solving quadratic equations and inequalities
2. Graphing quadratic functions
3. Finding the maximum or minimum of a quadratic function
4. Modeling real-world phenomena, like projectile motion
#quadraticequation #quadratic #maths #11thmath #completingsquare

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