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Quadratic Functions

Quadratic Functions

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Quadratic Functions

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  1. Quadratic Functions Taylor H. Asia J. Period 1 :)

  2. Definition ; • Quadratic function; a function that can be described by an equation of a form f(x)=ax^2+bx+c

  3. Examples; • f(x) = -2x2 + x - 1 • f(x) = x2 + 3x + 2 • f(x) = x2 + 2x - 3 • g(x) = 4x2 - x + 1 • h(x) = -x2 + 4x + 4

  4. Quadratic equations not only described the orbits along which the planets moved round the Sun, but also gave a way to observe them more closely. Real World Examples

  5. Building a 72-story skyscraper like Trump Tower in New York City is no easy feat. That’s where structural engineers like Ysrael Seinuk come in. This movie explains how shapes are at the foundation of structural engineering Real World Examples 2

  6. The science of optics teaches us how to make "bigger eyes", and if you want to look at something very far away, or very faint, you're going to need a really huge eye--such as the one used at Kitt Peak by astronomers studying distant galaxies Real World Examples 3

  7. Nature Examples

  8. Quadratic Equations An example of a Quadratic Equation: The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2). It is also called an "Equation of Degree 2" (because of the "2" on the x) The Standard Form of a Quadratic Equation looks like this: Here are some more examples: Nature Examples Hidden Quadratic Equations! So the "Standard Form" of a Quadratic Equation is ax2 + bx + c = 0 But sometimes a quadratic equation doesn't look like that! For example: How To Solve It? The "solutions" to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in the graph above). They are also called "roots", or sometimes "zeros" There are 3 ways to find the solutions: 1. You can Factor the Quadratic (find what to multiply to make the Quadratic Equation) 2. You can Complete the Square, or 3. You can use the special Quadratic Formula: Just plug in the values of a, b and c, and do the calculations. We will look at this method in more detail now.

  9. Nature Examples

  10. Graphs Of Functions

  11. Graphs Of Functions

  12. Graph Of Quadratic Function

  13. Sources • www.math.com

  14. Sources • www.algebra.com

  15. Sources • www.analyzemath.com