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Mastering Quadratic Functions: Test Essentials and Problem Solving

This comprehensive guide covers quadratic functions, including finding roots through factoring, completing the square, and the quadratic formula. It discusses forms of quadratic functions, graphing methods, and solving equations and inequalities. Key topics include vertex calculations, graph transformations, and solving systems of quadratics. The practical applications are highlighted through real-life examples, making it a valuable tool for mastering quadratic functions.

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Mastering Quadratic Functions: Test Essentials and Problem Solving

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  1. Quadratic Functions Accelerated Math II October 1, 2013

  2. One-Minute Question If f(x) = 3x2 + 6x, state the vertex of f(x).

  3. One-Minute Question If f(x) = 3x2 + 6x, state the vertex of f(x). x= and f(-1) =3 – 6 = -3, so (-1, -3)

  4. What would you put on a test covering quadratic functions? How do you find their roots? Factoring Completing a square Quadratic formula

  5. What would you put on a test covering quadratic functions? How do you find the x values of their vertices? Average their roots Completing a square Calculate –b/(2a)

  6. What would you put on a test covering quadratic functions? How do you find the y value of their vertices (maximum or minimum value)? Completing a square Calculate f(-b/(2a))

  7. What would you put on a test covering quadratic functions? What are different forms of a quadratic function? Standard: y = ax2 + bx + c Vertex: y = a(x – h)2 + k Factored or intercept : y = a(x – r1)(x – r2)

  8. What would you put on a test covering quadratic functions? Can you switch from form to form algebraically??

  9. How do you graph a quadratic function? • y = x2 • y = x2 + 4 • y = (x + 3)2 • y = 2(x – 3)2 + 5 • What’s the vertex of y = a(x – h)2 + k ?

  10. What would you put on a test covering quadratic functions? What affects the shape of their graph? “a” vertically stretches or shrinks or inverts. “h” translates horizontally. “k” translates vertically.

  11. What would you put on a test covering quadratic functions? What equation would produce this graph?

  12. How do you solve quadratic equations? • X2 + 15 = 79 • (X + 4)2 - 14 = 11 • X2 + 6x = 7 • 2x2 = 7x + 15 • Find the roots of f(x) = x2 + 2x – 35

  13. How do you solve harder quadratic equations? • X2 + 15 = 9 • (X + 4)2 - 10 = 11 • X2 + 6x = 5 • 2x2 = 7x + 10 • Find the roots of f(x) = 3x2 + 2x – 35

  14. How do you solve harder quadratic inequalities? • X2 + 18 > 9x • (X + 4)2 - 10 < 15 • X2 + 6x < 5 • y > 2x2 - x - 10 • y < -x2 + x + 12

  15. How do you solve systems of quadratics? Y = x2 + 3x – 7 Y = 2x2 - 5

  16. APPLICATIONS!! • See book…

  17. Logic about Quadratics • IF f(x) = 2x2 + kx – 20 has one root at 4, find its other root.

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