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Math I

Math I. UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored? Standard: MM2A4.b. DAY ONE. We will get x squared by itself. Then we will take the square root of both sides of the equal sign.

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Math I

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  1. Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored? Standard: MM2A4.b.

  2. DAY ONE

  3. We will get x squared by itself. Then we will take the square root of both sides of the equal sign. There will be a positive answer and a negative answer.

  4. Let’s look at some examples where x2 is already by itself.

  5. Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. Here, all we have to do is take the square root of both sides.

  6. Let’s look at some examples where x2 is NOT by itself.

  7. We must solve to get x2 by itself 1st! add 48 divide by 3 take the square root of both sides

  8. We must solve to get x2 by itself 1st! subtract 32 take the square root of both sides

  9. You try!

  10. Falling object model When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model:

  11. An engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking (s = starting height). Find the time (t) it will take for the egg to hit the ground (height = ? ). Disregard air resistance. The starting height is 32 feet. SOLUTION: Now, substitute 0 for h and solve. Subtract 32 from both sides Divide both sides by –16 Take the square root of both sides So, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!! 

  12. DAY TWO

  13. Warm-up The following quadratics are in standard form, ax2 + bx + c Evaluate b2 – 4ac for each of the following 1 • x2 – 3x + 2 • x2 – 4x + 4 • 2x2 – 3x + 3 0 -15

  14. The discriminant is a small part of the quadratic formula. notes There is a way to tell how many roots an equation will have. It’s called finding the discriminant.

  15. If the answer is POSITIVE, then you will have 2 roots. If the answer is ZERO, then you will have 1 root. If the answer is NEGATIVE, then you will have no roots. Our text book says solutions instead of roots (same thing).

  16. Determine the number of roots.Example: 1 No Roots

  17. Determine the number of roots.Example: 2 1 ROOT

  18. Determine the number of roots.Example: 3 2 ROOTS

  19. Find the number of x-intercepts.Example: 4 two x-intercepts

  20. Find the number of x-intercepts.Example: 5 zero x-intercepts

  21. Solve for x:

  22. Quadratic Formula: gives the solution of in terms of the coefficients a, b & c. The solutions of the quadratic equation are

  23. 1st 2nd Ex: 1 Solve x2+ 9x +14 = 0 a = b = c =

  24. example #2 1 and 3

  25. Try these on your own: -5/2 & 2 -1 & 4 2.89 & -1.39

  26. Rocket A rocket is shot upward with an initial velocity of 125 feet per second from a platform 3 feet above the ground. Use the model to find how long it will take the rocket to hit the ground. t = 7.83 seconds 3 ft

  27. HOMEWORK 

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