Ch 1+2: Factoring + Radicals
Expand and simplify (x+1)(x+2)(2x-1)
2x3+5x2+x-2
A quadratic function has a vertex at (6,-2) and a negative 'a' value, when in standard form. How many x-intercepts will the graph have?
None
solve 2(x+2)2=42
-2-√21
-2+√21
If sinθ < 0 and tanθ >0, which quadrant does θ lie in?
III
What's Ms. Li's favorite (sub)topic in Pre-Calc 11? (2 possible ANS)
Trig- ambiguous case
Factoring- completing the square
Simplify: √27 + 2√12 - 3√8
-6√2 + 7√3
Determine the following characteristics for the quadratic function y=-2(x-4)2 +3 -vertex -equation of axis of symmetry -direction of opening -domain -range
(4, 3) x=4 downward xER y is greater than or equal to 3
For what value of k does the equation x2 +9x+k=0 have one real root?
k=20.25
Determine the exact value of sin 210 (no calc!)
-1/2
What were Ms. Li's TWO favorite subjects in high school?
music and math
Give an example of a conjugate and its use when dealing with simplifying radicals
ex: x - 1 and x+1 are conjugates, gives difference of squares and NO middle term
Determine a quadratic function in standard form form that has the given characteristics. its vertex at (2,0) and passes through the point (1,3)
y=3(x-2)2
Solve the function y=5x2 +20x -6 by completing the square
x=-0.28, 4.28
The terminal arm of angle A passes through the point R(-15, -8). Determine the distance from the origin to point R and Determine the value of sin A (NO CALC!)
r=17 sinA=-8/17
Name all the languages Ms. Li can speak (4)
English, Cantonese, Mandarin, French
Rationalize the denominator:
(√7 - √3)
(√7 + √3)
7 - 2√21 + 3
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4
Change to equation y=2x2 +4x+4 to standard form
2(x+1)^2 +2
Solve the function 3x2 +19x -14=0 by using the quadratic formula
x=-7, 2/3
In triangle ABC, angle A is 40 degrees, side a is 10cm and b=15cm. Determine the number of possible triangles that can be drawn or whether the triangle does not exist. Sketch a diagram to represent the possible triangles. If the triangles exists, determine the measure of angle B to the nearest tenth of a degree
two triangles exist angle B=74.6 or 105.4 degrees
What is Ms. Li's BBT topping of choice?
pudding
Factor completely: 12(x+2)2 +24(x+2) +9
3(2x+7)(2x+5)
Determine the vertex, axis of symmetry, direction of opening domain, range, #of x-intercepts and the value of the y-int for the equation y=0.5x2 -6x-3
(6,-21) x=6 upward xER y is greater than or equal to -21 2 x-ints (0,3)
Two numbers have a difference of 10. Write an equation showing that the sum of their squares is 212.
(x)2 + (x+10)2 = 212
Given cosA=(√ 2/2), the largest value of A is_____degrees?
315 degrees
What is Ms. Li's favorite drink?
water