Mathematics Dictionary
Figure 36 ABG Program 07 05
Subject : Solve abs(a*x^2 + B*x + c) = d

Q1. Solve abs(x^2 - 6*abs(x) + 8) = 3 graphically
A1. Solve abs(a*x^2+b*abs(x)+c)=d is in ABH Program 07 05. To get the answer from graph, we should start Program ABH and give the values of a,b,c,d. For this example we give 1, -6, 8, 3. From the diagram then can find the answer.


Q2. Solve abs(x^2 - 6*abs(x) + 8) = 3
A2. Solution : We should solve 4 quadratic equations
  • x^2-6*x+8 = +3
  • x^2+6*x+8 = +3
  • x^2-6*x+8 = -3
  • x^2+6*x+8 = -3
Then use quadratic formula we can find the real roots. The solutions are the intersections of y = abs(x^2 - 6*abs(x) + 8 and line y = 3


Q3. How many intersection of y=abs(x^2 - 6*abs(x) + 8) and y = 8
A3. Solution : We should solve 4 quadratic equations
  • x^2-6*x+8 = +8
  • x^2+6*x+8 = +8
  • x^2-6*x+8 = -8
  • x^2+6*x+8 = -8
Then use quadratic formula we can find the real roots are 6, 0, 0, -6. The intersections of y = abs(x^2 - 6*abs(x) + 8 and line y = 8 are 3. If we use discriminant method the answer may give as 4 because there are duplicate roots 0. Four real roots answer is correct but 4 intersections answer is wrong.
Solution on internet

Exercises : Use Program ABH program 07 05 and give the values of a,b,c,d.
  • How many real solutions in abs(x^2 - 6*abs(x) + 8) = 0.5
  • How many real solutions in abs(x^2 - 6*abs(x) + 8) = 8
  • How many real solutions in abs(x^2 - 6*abs(x) + 8) = 9
  • How many real solutions in abs(x^2 - 2*abs(x) - 3) = 3
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