# How to Solve a Quadratic Equation by Graphing?

Different methods are used to solve quadratic equations. This step-by-step guide teaches how to solve a quadratic equation by graphing.

**Related Topics**

- How to Solve a Quadratic Equation by Completing the Square?
- How to Solve a Quadratic Equation by Factoring?

**A step-by-step guide to** **solving a quadratic equation by graphing**

Solving quadratic equations means finding the variable’s value (or values) that satisfies the equation. The values that satisfy the quadratic equation are known as the root (or) solution (or) zero. Since the degree of a quadratic equation is \(2\), it can have at most \(2\) roots.

There are different ways of solving quadratic equations:

- Solving quadratic equations by factoring
- Solving quadratic equations by completing the square
- Solving quadratic equations by graphing
- Solving quadratic equations by quadratic formula

To solve quadratics by graphing, we must first graph the quadratic expression (when the equation is in standard form) by hand or using a graphing calculator. Then the \(x\)-intercept(s) of the graph (the points) that intersect the \(x\)-axis of the graph) are nothing but the roots of the quadratic equation.

**Solving a Quadratic Equation by Graphing – Example 1:**

Solve the following quadratic equation using graphing. \(3x^2 + 5 = 11x\)

**Solution:** First, convert the given equation into the standard form, \(3x^2-11x+5=0\). Now, graph the quadratic function \(y= 3x^2 – 11x + 5\) manually or using a graphing calculator and determine the \(x\)-intercepts.

Thus, the solutions of the quadratic equation \(3x^2 + 5 = 11x\) are \(0.532\) and \(3.135\).

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