Flashcards

quadratics

Lance Erickson English 27 cards

Cards in this deck (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.