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19 • Parabola. This is what anything with an x2 in it looks like graphed. • The bottom (or top) is the vertex. (Also called the minimum or maximum point). Scientific Notation on TAKS 20 If Jupiter is GREATER than the earth, are you going to multiply or divide by 11.2 to find earth?_____ So _______ 8.9 by 11.2 and you get ____ x 104 And now change that to scientific notation. QQ11 22 21 Combined? Do you add, subtract, multiply or divide? _____ Show work: Which don’t open up? _____ and ____ Graph the other two…which is widest: _____________ 23 Looks can be deceiving. QQ12 Reading a Quadratic Graph This was on the benchmark 24 What is the “c’ value of this parabola? (also known as the y intercept?)_____ What does that mean???? ________ ______________________________ How high was the baseball when it was first thrown?_______ When does the baseball approach 80 meters for the first time? ______ When does it approach the 80-meter mark again? _____ How much time has passed between these two points?_____ Therefore, which is the correct answer?____ 25 QQ13 Look at the equation. The “c’ value is the y intercept. You write that ( , ). Eliminate ____ and ______ An x intercept always begins with a number. That eliminates _____ Answer?______ 26 Does domain refer to the x-values or the yvalues?_____ What is the smallest x-value on the graph?____ Is this value actually included in the domain?____ Why or why not? ________________________ What is the largest x-value on the graph?____ Is this value actually included in the domain?____ Why or why not? ______________________ Now, which would be the range if the x were changed to “y’?_________________ 27 QQ14 Answer the same questions for this problem as the last one. Smallest x_______ Largest x_________ Now, what is the range is x was changed to “y”?____________ 28 Simplification the easy way…use your calculator Put the problem at y1 and an answer at y2. look at the table. If the y columns are the same…you won. Using Math: 29 Using math: But this one has a and b in it. Okay, make a = 2 and b = 3 and simplify to an number answer.. Then use a=2 and b= 3 in the answers and see which gets you the same answer. Numbers first: (__ *___) /___ =____ Eliminate ___ and ___ Now do your exponents. Just doing “a’ will get your answer. Why?_____ 30 QQ15 Quadratics For TAKS Three Methods on this page • • • • • • (2x +3) (5x -9) (multiply) 2x1 + 3 Times 5x1 - 9 -18x -27 10 x2 +15x _ 10x2 -3x -27 • Do this like an old fashioned multiplication problem Multiply -9 times 3 = 27 Multiply -9 times 2x = 18x Multiply 5x times 3 = 15x Multiply 5x times 2x = 10x2 . Add -18x and +15x = -3x • • • • • • • • • TAKS TIP Put the problem in the calculator at Y1 Put an answer at Y2 Press 2nd graph of table. If ALL the y values match…it is correct. • Or FOIL • 10x2 -18x _+15x _-27__ • F O I L • First Outside Inside Last • • -3x__ OI • Combine Outside and inside • Answer: 10x2 -3x - 27 • • • • • • • ( 2x + 3 ) (5x -9) First 2x * 5x = 10x 3rd Outside 2x * -9 = -18x Inside 3 * 5x = 15x Last 3 * -9 = -27 Combine Outside and Inside -18 x + 15x = -3x QQ1 Quadratics 32 Draw it: 31 Formula for Area:________ Length = ___________ Width = _____________ Pick a method from page QQ1___ Find the answer. Show work. Formula for area:____________ Length______________ Width______________ Use a different method from problem number one. Show work QQ17 33 34 Y = method????? First, circle the zeros and state them here: x =____ and x = __ Three Ways: 1. Foil each answer, get an equation and graph it. (yuk…lots of work) 2. Enter each answer as is on the calculator and graph…easy In both, look at the graph….If that does not help, look at the table for the x values where y = 0. 3. Set each factor = to zero and solve. Those should be your x values. 35 QQ18 36 37 Change to decimals • • • • Tough one. Any ideas???? First graph it. Does it look like it is symmetrical around the y axis??? Would a and b be symmetrical? _____ How about arithmetic? For c and d…plug them in…which one works for both answers? • • Graph it. Or substitute the answers in. Just do it. QQ19 QQ20