Module 3: Lesson 1

 

Self-Check 4

1.  
   

   2. f(x) = −x2 + 7x − 10

       

      Step 1: Determine the end behaviour by looking at the degree of the polynomial and the sign of the leading coefficient.
      
      The degree of the polynomial is even and the leading coefficient is negative, so the graph will start in quadrant 3 and end in quadrant 4.

       

      Step 2: Factor the polynomial if it is not given in the problem.
      
      In this case, f(x) = −x2 + 7x − 10 becomes
      
      

       

      

       

      Step 3: Determine the x-intercepts by looking at the factors of the polynomial.
      
      The x-intercepts are x = 5 and 2.

       

      Step 4: Determine the y-intercept by substituting zero into the function.
      
      The y-intercept occurs at the point (0, −10).

       

      Step 5: Determine the nature of the x-intercepts (whether there is a sign change) by looking at the multiplicity of the polynomial’s factors.
      
      Each factor has a multiplicity of 1, so the function will change signs at the corresponding x-intercepts.

       

      Step 6: Draw a smooth curve through the x- and y-intercepts.
      
      

       
      
      

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