14.4 Converting from general to vertex form by completing the square

In previous chapter, we learned all about factoring quadratic equations. There are a lot of applications of quadratic equations like calculating possible profits, computing for area. There are a lot of interesting uses of quadratic equations too, and there’s an interesting article about 101 uses of quadratic equation. Now in this chapter, we will get to learn more about Quadratic functions especially on its characteristics, and its general form.

We will learn in this chapter that Quadratic Functions have a parabolic graph. The parabola may open down, or may open up. The peak of the parabola is called the vertex. If the parabola is opening down, then the vertex is the highest point or the maximum. If the parabola opens down then the vertex is the lowest point or the minimum. The line that passes through that vertex is called the axis of symmetry. It also has an x intercept, where y=0, and the y intercept where x=0.A quadratic equation also have a domain and a range. The domain is simply the x values, and the range is the y values.

We will also learn more on the general form of the quadratic function, f(x)=ax2+bx+cf(x) = ax^2 + bx + c in Not every quadratic function that you would come across to would look the same, and there would be times that you would need to transform them into the general form to make solving them easier.

Apart from learning about the characteristics and the general form of quadratic function, we will also learn how to graph a quadratic function and at the same time learn how to identify the equation used in the graph given.

Converting from general to vertex form by completing the square

Lessons

Notes:
Step-by- step approach:
1. isolate X’s on one side of the equation
2. factor out the leading coefficient of X2X^2
3. “completing the square”
• X-side: inside the bracket, add (half of the coefficient of X)2X)^2
• Y-side: add [ leading coefficient (half of the coefficient of X)2X)^2 ]
4. clean up
• X-side: convert to perfect-square form
• Y-side: clean up the algebra
5. (optional)
If necessary, determine the vertex now by setting both sides of the equation equal to ZERO.
6. move the constant term from the Y-side to the X-side, and we have a quadratic function in vertex form!
Teacher pug

Converting from general to vertex form by completing the square

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