 ## Solving Quadratics by Looking at their Graphs

We can solve quadratics by looking at their graphs. By using and looking at the equation, we can generate accurate graphs that will tell us the approximate solution(s) to a quadratic. We can use this method with or without a graphic calculator.
ULTIMATE MATHS
WHERE MATHS IS AT YOUR FINGERTIPS!

## Solving Quadratics Graphically without a Graphic Calculator

If you do not have access to calculator, you can still solve quadratic graphically. To do this, we need to understand that y=0 (the 0 in the quadratic equation). Since the x axis is y=0, any point where the line of the parabola crosses the x-axis is a solution. The first step is to replace the x in the quadratic with different values of x on the graph which allows you to find different co-ordinates the line passes. To do this, you should construct a table. We will be trying to solve the following quadratic equation. Step 1: Finding the value of y in relation to x Use the equation to calculate values of y in relation to x. Step 2: Use these values to sketch an accurate graph You have now got 9 co-ordinates. Plot them on a graph and join them so that you have a parabola. We have used a professional graphing software, but the same also works on paper. Step 3: Find the solution(s) The last step is to find the solution. Since y=0, the solutions are all the points on the x axis. In this case we have two. -3 and 4. These are the solutions that you would have otherwise found through factorisation or by using the quadratic formula.  ## Solving Quadratics Graphically with a Graphic Calculator

If you have access to a graphic calculator or a graphing software, you can solve the quadratic equation a lot quicker. Just enter y=(quadratic equation). Then the exact parabola will be drawn for you. Using the tracing function, you can then identify the exact points where the parabola cross the x-axis. These points are the solutions. The reason why using a graphic calculator or graphing software is better is because sometimes, the parabola will not cross the x-axis at whole numbers and then it can be very difficult to find the exact answer. ULTIMATE MATHS Becoming an Accomplished Mathematician Ultimate Maths is a professional maths website that gives students the opportunity to learn, revise and apply different maths skills. We provide a wide range of lessons and resources...  Quality Content A wide range of quality learning resources is at your disposal. Effective Teaching Explanations, examples and questions combined for an effective learning experience. Easy Navigation A simple user interface ensures that you find the topics you are looking for.       Chapter 17.3:  Learning Outcomes Students will learn how to solve a quadratic by considering its graph (without a calculator)! Students will learn how to solve quadratics using their graphic calculators!    ## NOT CURRENTLY AVAILABLE! 