Download
solving quadratic equations by finding square n.
Skip this Video
Loading SlideShow in 5 Seconds..
Solving Quadratic Equations by Finding Square Roots PowerPoint Presentation
Download Presentation
Solving Quadratic Equations by Finding Square Roots

Solving Quadratic Equations by Finding Square Roots

234 Vues Download Presentation
Télécharger la présentation

Solving Quadratic Equations by Finding Square Roots

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Solving Quadratic Equations by Finding Square Roots

  2. Inverse Operations… The opposite of + is - The opposite of is The opposite of x2 is Square Root of a Number: If b2 = a, then b = (b is a square root of a)

  3. Radical Symbol : Radicand: number inside the radical

  4. All positive numbers have two square roots. POSITIVE OR NEGATIVE Positive square root of a Negative square root of a

  5. Perfect Squares:KNOW 1-20 and their square roots. Perfect Squares: 1,4,9,16,25,36,49,64,81,100, 121, 144,169,196,225,256,289,324, 361,400

  6. In algebra and geometry, we usually leave answers in radical terms (rationalize). Pull out perfect squares, leave what's left inside the radical

  7. Square Root Rules Refresher: To square root a fraction, square root the numerator and denominator separately “square root of top goes on top, square root of bottom goes on bottom”

  8. Quadratic equation: is x to the second power Standard Form of Quadratic Function: ax2+bx+c=0

  9. Today we will Find Solutions when there is not a bxterm ax2+c=0 Isolate x2 (Get x2 alone in form x2=d) Once you get x2=d take the square root of both sides to get x.

  10. 3 Results 1. x2=dIf d is a positive number, then you have 2 solutions 2. x2=dIf d=0 then there is only one solution x=0 3. x2=dIf d is a negative number, there is no solution (Can’t take sq. root of a negative)

  11. Examples: 2. x2=5 1. x2=4 2 2 x can be + or -, when squared it is positive

  12. Solve: 4x2 + 100 = 0 -100 -100 4x2 = -100 (divide both sides by 4) x2 = -25 NO Solution

  13. 3x2-99 = 0 3x2 = 99 x2 = 33 Two Solutions

  14. 2x2-126 = 0 2x2= 126 x2 = 63 rationalize Two Solutions

  15. The surface area of a cube is 150ft2. Find the length of each edge. SA = 6s2 x 1st DIVIDE BY 6 150 = 6s2 25 = s2 x x Sides of the cube are 5 ft. You can’t have a negative length.

  16. Watch out below! A construction worker on the top floor of a 200 foot tall building accidentally drops a heavy wrench. How many sections will it take to hit the ground? The formula d=rtis used when the speed is constant. However, when an object is dropped, the speed continually increases. Use the formula: h = -16t2 + s h = final height of object t = time s = starting height of object h = -16t2 + s 0 = -16t2 + 200 -200 = -16t2 12.5 = t2 √12.5 = t About 3.54 seconds.