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Mastering Quadratics: Solving and Factoring Techniques

Dive deeper into quadratic equations with a sequel to "teach me how to factor." Learn to solve quadratics using graphing and factoring methods, understand the importance of identifying solutions, roots, x-intercepts, and zeros. Practice solving quadratic equations by factoring, and explore real-world applications like projectile motion. Enhance your skills by writing quadratic functions in standard form with specific zeros. Take your math prowess to the next level!

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Mastering Quadratics: Solving and Factoring Techniques

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  1. 4.1 Solving Quads by graphing and factoring

  2. Ahh…the sequel to “teach me how to factor” • Do the Quad Solve • Ms. G distributes the overview sheets

  3. Just an overview of where we’re going

  4. First, vocabulary solutions roots X-intercepts zeros These all mean the same thing when solving quadratics…KNOW THIS!!!

  5. Can we use a table of values to solve? • Keep in mind, you’re looking for the x-intercepts. These occur when y = 0! • Find the zeros of the function from a table

  6. From a graph (we’ll learn to graph a little later)

  7. Solving by factoring • Easiest method to use, if the quadratic is factorable • Steps: • Set function equal to 0 • Factor • Set each factor equal to zero and solve

  8. Application • When an object is launched into the air, such as a soccer ball, it is called a projectile. There is a general function that approximates the height (h) of a projectile on Earth after (t) seconds Constant due to Earth’s gravity Initial velocity Initial height

  9. A golf ball is hit from the ground with an initial velocity of 80 ft/sec. After how many seconds will the ball hit the ground?

  10. Writing a function • Write a quadratic function in standard form with zeros 4 and -7

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