Lesson 10.6 and 10.7 – Quadratic Formula and the

Lesson 10.6 and 10.7 – Quadratic Formula and the Discriminant Let’s look at the quadratic formula:

The expression

is called the Discriminant

Because it is located under the radical sign, we can use the value of the Discriminant to determine the number of solutions for the quadratic equation.

Think about what we know about taking the square root. If we take the square root of a: Positive numbers there are ______solutions. Negative numbers there are _____solutions. Zero there is ____solution.

Using the discriminate of Value of the discriminate Number of Solutions

Graph of

Find the number of solutions

1. Write the equation in standard form 2. Find the value of the Discriminant

Find the number of x-intercepts

Tell whether the equation has one solution, two solutions, or no solutions.

Find the number of x-intercepts of the graph of the function.