Interpret the Discriminant Section 10.7

Objectives: Use the value of the discriminant to describe solutions and intercepts of a quadratic equation

Key Vocabulary: Discriminant

Discriminant

Using the Discriminant

Example 1: Use the discriminant to describe the number of solutions. .

Example 2: Use the discriminant to describe the number of solutions.

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

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

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

Example 3: Find the number of x-intercepts of the graph of the function.

#4: Find the number of x-intercepts of the graph of the function.

#5: Find the number of x-intercepts of the graph of the function.

#6: Find the number of x-intercepts of the graph of the function.

Example 4: The Centennial Fountain in Chicago shoots a water arc that can be modeled by the graph of the equation where x is the horizontal distance (in feet) from the river’s north shore and y is the height (in feet) above the water. Does the water arc reach a height of 50 feet? If so, about how far from the north shore is the water arc 50 feet above the water?

Homework Assignment Page 681 #8, 10, 12, 14, 16, 18, 22, 24, 30, 32, 34, 38, 46, 48