University:
Ontario Virtual School
Course:
MBF3C | College Preparation
Academic year:

2023
Views:

26

Pages:

5
Author:

anon

The Quadratic Relation Complete 2 The Quadratic Relation 𝑦 = 𝑎𝑥 + 𝑘 2 Recall that any quadratic function has an 𝑥 – term 2 The simplest quadratic functions is 𝑦 = 𝑥 2 Example 1: Graph 𝑦 = 𝑥 using a table of values x -2 -1 0 1 2 y 4 1 0 1 4 2 For 𝑥 =− 2, 4 = (− 2) = 4 and so on… Note the step pattern: 2 ( 2 2 ) 1, 4, 9, … 1 , 2 , 3 , … Vertical Stretch: The effect of changing a. Example 2: Graph each of the following functions using a graphing calculator. Keep t 2 he graph of 𝑦 = 𝑥 2 a) 𝑦 = 2𝑥 b) 𝑦 = 1 2 2 𝑥 How are the graphs the same? How are they different? The graphs are at the same position but are stretched vertically or wider depending (thinner or inner or wider on the coefficient of the x²-term, a) The graph of y=2x² (Note: a=2>1) is vertically compressed (thinner) compared to the graph of 𝑦 = 𝑥^2 The graph of 𝑦 = 1 2 2 𝑥 is vertically compressed (wider) compared to the graph of y=x? Reflection: Now, we will investigate when the value of a is negative. Example: Sketch the graphs of 2 a) 𝑦 = 𝑥 2 𝑦 =− 𝑥 2 b) 𝑦 = 2𝑥 2 𝑦 =− 2𝑥 How are the graphs the same? How are the different? They have the same shape but are at different positions. Points are reflected in the x-axis (flipped) What is the point mapping for this type of transformation? (x,y) → (x.ay) Ex: (2,4) → (2,-4) 2 Vertical Translation: The effect of changing k in 𝑦 = 𝑥 + 𝑘 Example: Graph each of the following functions using a graphing calculator. Graph th em on the same grid and also label each parabola with its equation 2 𝑦 =𝑥 2 𝑦 =𝑥 + 2 2 𝑦 =𝑥 − 2 How are the graphs different? How are they the same? The graphs have the same shape and size but are at different locations 2 What is the effect of adding a value of k to the basic function to get 𝑦 = 𝑥 + 𝑘. 2 If k>o, the points of 𝑦 = 𝑥 are shifted by k units upward. 2 If k0 (positive) then the parabola opens up 2 If a>1, then the parabola is thinner compared to 𝑦 = 𝑥 2 If -10, the vertex of the parabola is k units above the x-axis If k<0, the vertex of the parabola is k units below the x-axis 2 The coordinates of the vertex at 𝑦 = 𝑎𝑥 + 𝑘 are (0,k)

Mathematics: The Quadratic Relation Complete

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