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)
Radical Symbol : Radicand: number inside the radical
All positive numbers have two square roots. POSITIVE OR NEGATIVE Positive square root of a Negative square root of a
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
In algebra and geometry, we usually leave answers in radical terms (rationalize). Pull out perfect squares, leave what's left inside the radical
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”
Quadratic equation: is x to the second power Standard Form of Quadratic Function: ax2+bx+c=0
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.
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)
Examples: 2. x2=5 1. x2=4 2 2 x can be + or -, when squared it is positive
Solve: 4x2 + 100 = 0 -100 -100 4x2 = -100 (divide both sides by 4) x2 = -25 NO Solution
3x2-99 = 0 3x2 = 99 x2 = 33 Two Solutions
2x2-126 = 0 2x2= 126 x2 = 63 rationalize Two Solutions
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.
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.