quadratics

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Flashcards on quadratics , created by Lance Erickson on 19/02/2017.
Lance Erickson
Flashcards by Lance Erickson, updated more than 1 year ago
Lance Erickson
Created by Lance Erickson over 7 years ago
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Question Answer
The 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.
The 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"
The 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.
Solve for x. since you have x^2 and x you need to use formula (try factor). first step is get " = 0"
solve for x add 8 , divide by 2, square root +/- then add 3
solve for x. no work to do. x = 1 and - 1/2
find x intercepts 0! put 0 into y to get above equation and solve
name 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)
The 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)
what 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)
convert to standard form. First FOIL. Second distribute in 3. Third, collect like terms. Notice that "a" is the same in both.
solve for x. you can not just "read" the answer. FOIL then get " = 0" then formula (factor if lucky)
solve for x. Notice "= 0" so x = 0, x = -2, x = 7
What 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)
solve graphically graph y = 0 and y = 3x(x+2)(x-7). Find the point(s) of intersection and take only the x coordinate.
solve 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.
The 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)
vertex? start with x = -b/2a then sub. into f(x) for y coordinate.
line of symmetry? you need the x coordinate of the vertex. x = -b/2a
solve by completing the square 1) = 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
what 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
is 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
simplify 1 - (-1) + (-i) = 2 - i
simplify use the conjugate 2 - 3i. final answer: 1/11 + 18i/11 please let me know if this is wrong.
find the equation for the parabola shown put vertex into the equation and sub. in a point (0,3). y = - 2(x-1)^2 +5
when 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
what 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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