Unit 2 Reciprocals of Quadratic Functions by 1azye https://padlet.com/cjxl2zy96/moz10uzpit3432kl en-us 2023-10-02 03:11:51 UTC 2023-10-02 16:59:38 UTC hello@padlet.com What is Reciprocal? cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727958266 The reciprocal is basic the numerator and denominator flipped
For example: If we have a fraction 1/3, then the reciprocal will be 3/1, if we have a 3/4, we will have 4/3.]]> 2023-10-02 04:10:28 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727958266 Rational functions can be analysed using key features: asymptotes, intercepts, slope (positive or negative, increasing or decreasing), domain, range, and positive and negative intervals. cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727960020 2023-10-02 04:13:40 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727960020 The main formula of the reciprocal of the quadratic function is y = 1/x^2, and x can not be 0. cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727971928 2023-10-02 04:33:23 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727971928 Reciprocals of quadratic functions with two zeros have three parts, with the middle one reaching a maximum or minimum point. This point is equidistant from the two vertical asymptotes. cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727977393 2023-10-02 04:40:44 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727977393 Lets see a example with the equation y = x^2, so the reciprocal is y=1/x^2 cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727988502
  • There are no zeros, so no vertical asymptotes.
  • The quadratic is positive, so the reciprocal will also always be positive.
  • The y-intercept of 
    y = x^2 is 0, so the reciprocal at this point is undefined.
  • As x becomes very large or very small, y approaches 0.
  • The vertex of 
    y = x^2 is at (0,0), which means the reciprocal function has a minimum value at x = 0, but it is not defined at this point.

    • ]]>     2023-10-02 04:56:20 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727988502     Example question 1: Consider the function f(x) = 2/x^2 - 4 cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727998060 a) State the domain
    b) Find the equation of the asymptotes
    c) Describe the behaviour of the function near the asymptotes.]]>     2023-10-02 05:07:04 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2727998060     Answer : cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2728001286 a) Factor the denominator 
    x^2 - 4 = (x+2)(x-2)
    State the restrictions 
    x doesn’t = 2, -2
    Domain: {x doesn’t = 2, -2 | xER}

    b) Vertical asymptotes x= 2, -2
         Horizontal asymptote y = 0

    c) look at the image]]>     2023-10-02 05:11:19 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2728001286     Question 2: stretch the previous equation cjxl2zy96 https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2728006237 2023-10-02 05:18:08 UTC https://padlet.com/cjxl2zy96/moz10uzpit3432kl/wish/2728006237