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Big Ideas Math Algebra 1 A Bridge to Success
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Big Ideas Math Algebra 1 A Bridge to Success View details
3. Solving Quadratic Equations Using Square Roots
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Exercise 4 Page 497

The x-intercepts of a graph are the solutions of the associated equation.

See solution.

Practice makes perfect

We can solve a quadratic equation, ax^2+c=0, by graphing its associated quadratic function f(x) = ax^2+c and identifying the x-intercepts of the graph. These are the solutions to the quadratic equation.

Therefore, we can tell the number of solutions that the quadratic equation has by counting the number of times that its associated function intersect the x-axis. Let's review the effects of the parameters a and c in the function f(x)=ax^2+c.

  • If a>0, the parabola opens up.
  • If a<0, the parabola open down.
  • If c>0, the parabola is translated up by c units.
  • If c>0, the parabola is translated up by |c| units.
  • If c=0, the parabola has its vertex at the origin.
With this in mind, we can predict the number of times the parabola will intersect the x-axis, and therefore the number of real solutions of ax^2+c =0. We can see this being illustrated in the graph below. Give it a try.
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arrow_right Communicate Your Answer p.497
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arrow_right Monitoring Progress p.499-500
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arrow_right Exercises p.501-502
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