14.1 Graphical Solution of Systems of Equations

  • Conic Sections • Parabola, Circle, Ellipse, Hyperbola • Solving Systems of Equations Graphically

In this section, we first discuss the graphs of the circle, parabola, ellipse, and hyperbola, which are known as the conic sections. We saw the parabola earlier when discussing quadratic functions in Chapter 7. Then we will find graphical solutions of systems of equations involving these and other nonlinear equations.

EXAMPLE 1 Calculator graph—parabola

Graph the equation y = 3x2 − 6x . 

We graphed equations of this form in Section 7.4. Because the general quadratic function is y = ax2 + bx + c ,  for y = 3x2 − 6x ,  we have a = 3 , b =  − 6 ,  and c = 0. Therefore,  − b / (2a) = 1 ,  which means ...

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