Back to: MATHEMATICS SS1

**Welcome to class! **

In today’s class, we will be talking about the solution of the quadratic equation by graphical method. Enjoy the class!

**The solution of Quadratic Equation by Graphical Method**

**Quadratic equation with two solutions**

We will now graph a quadratic equation that has two solutions. The solutions are given by the two points where the graph intersects the *x*-axis.

**Example:**

Solve the equation *x*^{2} + *x* – 3 = 0 by drawing its graph for –3 ≤ *x* ≤ 2.

**Solution**

Rewrite the quadratic equation *x*^{2} + *x* – 3 = 0 as the quadratic function *y = x*^{2} + *x* – 3

Draw the graph for *y = x*^{2} + *x* – 3 for –3 ≤* x* ≤ 2.

x |
–3 | –2 | –1 | 0 | 1 | 2 |

y |
3 | –1 | –3 | –3 | –1 | 3 |

The solution for the equation *x*^{2} + *x* – 3 can be obtained by looking at the points where the graph *y* = *x*^{2} + *x* – 3 cuts the *x*-axis (i.e. *y* = 0).

The graph *y* = *x*^{2} + *x* – 3, cuts the *x*-axis at *x * 1.3 and *x * –2.3

So, the solution for the equation *x* + *x* –3 is *x * 1.3 or *x * –2.3.

Recall that in the quadratic formula, the discriminant *b*^{2} – 4*ac* is positive when there are two distinct real solutions (or roots). **How to solve the quadratic equation by graphing?**

It uses the vertex formula to get the vertex which also gives an idea of what values to choose to plot the points. This is an example where the coefficient of *x*^{2} is positive.

**Quadratic equation with one solution**

**Example:**

By plotting the graph, solve the equation 6*x* – 9 – *x*^{2} = 0.

**Solution**

x |
0 | 1 | 2 | 3 | 4 | 5 | 6 |

y |
–9 | –4 | –1 | 0 | –1 | –4 | –9 |

Notice that the graph does not cross the *x*-axis, but touches the *x*-axis at *x* = 3. This means that the equation 6*x* – 9 – *x*^{2} = 0 has one solution (or equal roots) of *x* = 3.

Recall that in the quadratic formula, in such a case where the roots are equal, the discriminant *b*^{2} – 4*ac* = 0.

**Quadratic equation with no real solution**

**Example:**

Solve the equation *x*^{2} + 4*x + *8 = 0 using the graphical method.

**Solution**

x |
–4 | –3 | –2 | –1 | 0 | 1 |

y |
8 | 5 | 4 | 5 | 8 | 13 |

Notice that the graph does not cross or touch the *x*-axis. This means that the equation *x*^{2} + 4*x + *8 = 0 does not have any real solution (or roots).

In our next class, we will be talking about** the Idea of Sets.** We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

**How Can We Make ClassNotesNG Better? - CLICK to Tell Us Now!**

**Pass WAEC, JAMB, NECO, BECE In One Sitting CLICK HERE!**

**Watch FREE Video Lessons for Best Grades on Afrilearn HERE!💃**

favouriteThis is great

Makes reading easy