Solving Quadratic Equations by Graphing  Quadratic Equation- A quadratic function set equal to a value, in the form ax 2 +bx+c, where a≠0  Standard.

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Presentation transcript:

Solving Quadratic Equations by Graphing

 Quadratic Equation- A quadratic function set equal to a value, in the form ax 2 +bx+c, where a≠0  Standard Form- A quadratic equation written in the form ax 2 +bx+c, where a,b, and c are integers, and a≠0  Root- The solutions of a quadratic equation  Zero- The x-intercepts of the graph of a quadratic equation, the points for which f(x)=0

 Find the axis of symmetry  Find the ordered pair at the vertex  Make a table of values with the vertex in the middle  Plot the points from the table

 Real solutions are the points on the graph where it crosses the x-axis.  Y-value should always be 0  Solutions are in terms of x values

 After you have graphed the equation, if the parabola crosses the x-axis twice, you have two real solutions.

 After you have graphed the equation, if the parabola touches the x-axis, but does not cross it, then you have one real solution.

 After you have graphed the equation, if the parabola does not cross or touch the x-axis, then you have no real solutions.

 Turn Calculator on  Press y= button  Enter equation  Press GRAPH button  Press 2 nd button, then press TRACE button  Select option 2:zero  Select point on graph left of zero  Select point on graph right of zero  Press enter  Repeat steps 5-9 as needed

 (x+2)(x-5)  (x-1)(x+3)  (x-2)(x-3)  (x+1)(x+4)

 Use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist.  Sum is 5, product is -14  Sum is -8, product is 12  Sum is 4, product is 4

 Worksheet 5-2