In earlier chapters we've shown you how to solve quadratic equations by factoring. A quadratic equation as you remember is an equation that can be written on the standard form $$ax^{2}+bx+c=0,\: \: where\: \: a\neq 0$$ You know by now how to solve a quadratic equation using factoring. Another way of solving a quadratic equation is to solve it graphically. The
roots of a quadratic equation are the x-intercepts of the graph. Example Solve the equation $$x^{2}-3x-10=0$$ Graph the equation. This could either be done by making a table of values as we have done in previous sections or by computer or a graphing calculator. The parabola cross the x-axis at x = -2 and x = 5.
These are the roots of the quadratic equation.
We can compare this solution to the one we would get if we were to solve the quadratic equation by factoring as we've done earlier.
$$x^{2}-3x-10=0$$
$$\left ( x+2 \right )\left ( x-5 \right )=0$$
$$x=-2\: \: or\: \: x=5$$
- A quadratic equation has two roots if its graph has two x-intercepts
- A quadratic equation has one root it its graph has one x-intercept
- A quadratic equation has no real solutions if its graph has no x-intercepts.
Here you can get a visual of your quadratic function
Video lesson
Solve the equation graphically
$$x^{2}-3x-10=0$$
Related Topics:
More Lessons for Grade 9 Math
Math Worksheets
Examples, solutions, videos, worksheets, and activities to help Algebra students learn about how to solve quadratic equations by graphing.
Solving Quadratic Equations by Graphing Part 1
This video demonstrates how to solve quadratic equations by graphing.
First, a
quadratic equation is converted into a quadratic function.
Then, the variables are changed to x and y to graph on a coordinate plane.
The solutions are shown where the function crosses the x-axis. Roots, x-intercepts, and zeros are given as synonyms for solutions. Finding roots from a table of values is also demonstrated.
Solving
Quadratic Equations by Graphing Part 2
This video shows how to solve quadratic equations using the TI84 and TI83 series of graphing calculators. Five problems are worked out. The different steps are shown including converting quadratic equations into calculator ready graphable quadratic functions. The video shows how to examine in graph and table view what the solutions are. The case of having no solutions is shown as well as that of having only one solution.
- Show Step-by-step Solutions
Graphing quadratic equations
Graphing a parabola from an equation in standard form. Includes x-intercept, y-intercept, vertex, and
axis of symmetry.
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the
step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.