# Solve Quadratics Graphically

## 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.

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## 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.

## Sketching Quadratics

Next you should look at how to sketch quadratics. Using the equation and the solutions, you can create a very accurate graphical representation of any
quadratic equations. Please share this page if you like it or found it helpful!

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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!

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