Flashcards
quadratics
Flashcards do conjunto (27)
- 1The ml of oil in a tank as a function of time, x, in seconds is given. What is the minimum amount of oil in the tank?you need the y coordinate of the vertex. start with x = -b/2a then sub. into f(x) for y coordinate.
- 2The ml of oil in a tank as a function of time, x, in seconds is given. What time will the tank have 100 ml of oil?sub. 100 into f(x) then solve. since you have x^2 and x you need to use formula (try factor). first step is get " = 0"
- 3The ml of oil in a tank as a function of time, x, in seconds is given. How much oil is in the tank after 1 minute?you need to substitute into x. however, first convert 1 minute into seconds. so put 60 into x and calculate.
- 4Solve for x.since you have x^2 and x you need to use formula (try factor). first step is get " = 0"
- 5solve for xadd 8 , divide by 2, square root +/- then add 3
- 6solve for x.no work to do. x = 1 and - 1/2
- 7find x intercepts0! put 0 into y to get above equation and solve
- 8name all the things you can know from this equation.1) vertex is (3,-8) 2) range is [-8, infinity) 3) minimum is -8 4) line of symmetry is x = 3 5) f(x) is increasing (3 , infinity) and decreasing (- infinity , 3)
- 9The point A(3,-2) is on f(x). what is the image of this point under this transformation?h r s v
so x minus 2, y times 3 and finally y minus 4 which gives: A'(1,-10)
- 10what does this tell you?1) vertex is (-2, -4) 2) range is [-4, infinity) 3) minimum is -4 4) line of symmetry is x = - 2 5) f(x) is increasing (-2 , infinity) and decreasing (- infinity , -2)
- 11convert to standard form.First FOIL. Second distribute in 3. Third, collect like terms. Notice that "a" is the same in both.
- 12solve for x.you can not just "read" the answer. FOIL then get " = 0" then formula (factor if lucky)
- 13solve for x.Notice "= 0" so x = 0, x = -2, x = 7
- 14What does this tell you?1) vertex is (4, 2) 2) range is (-infinity, 2] 3) maximum is 2 4) line of symmetry is x = -4 5) f(x) is decreasing (4 , infinity) and increasing (- infinity , 4)
- 15solve graphicallygraph y = 0 and y = 3x(x+2)(x-7). Find the point(s) of intersection and take only the x coordinate.
- 16solve for x.solve then check intervals.
to solve, answers are x = 0, x = -2 and x = 7
Check intervals: example let x = 1 then
3(1)(1+2)(1-7)= -54 < 0 so (0,7 ) is part of answer.
- 17The point A(3,-2) is on f(x). what is the image of this point under this transformation?h r s v
y times -5 and x time 1/2 finally y plus 3 which gives: A'(3/2,13)
- 18vertex?start with x = -b/2a then sub. into f(x) for y coordinate.
- 19line of symmetry?you need the x coordinate of the vertex.
x = -b/2a
- 20solve by completing the square1) = 0 so move 5x - 1
2) move constant back to get -4
3) a= 1. move on.
4) add (b/2)^2 to both sides
5) factor and solve
- 21what can you see from the function?1) should be 4 x intercepts
2) should be 3 turning points
3) right side goes up
4) y intercept is -3
- 22is this function odd, even or neither?sub in -x and simplify. if the result is f(x) it is even. if it is the opposite of f(x)
(i.e. -f(x) )
otherwise it is neither
- 23simplify1 - (-1) + (-i) =
2 - i
- 24simplifyuse the conjugate 2 - 3i.
final answer:
1/11 + 18i/11
please let me know if this is wrong.
- 25find the equation for the parabola shownput vertex into the equation and sub. in a point (0,3).
y = - 2(x-1)^2 +5
- 26when do you need x = -b/2a?if it is in standard form and you want:
vertex or
vertex form or
line of symmetry or
minimum/maximum or
range or
where increasing/decreasing - 27what can you say about the discriminate?D > 0 since there are 2 x intercepts.
If D = 0 there is only 1 intercept
if D < 0 then there no intercepts and the solutions are imaginary.
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- Descrição
- FlashCards sobre quadratics , criado por Lance Erickson em 19-02-2017.
- Criado por
- Lance Erickson
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