Using the Discriminant to Graph Parabolas (3.14.3)

Question 1

• Quadratic equation: ax 2 + bx + c = 0.

Answer 1

• Quadratic equation: ax 2 + bx + c = 0.

Question 2

• Discriminant: b
2
– 4ac. Checking the value of the discriminant tells about the solutions:
• b
2
– 4ac > 0 indicates there are two real solutions.
• b
2
– 4ac = 0 indicates there is only one solution.
• b
2
– 4ac

Answer 2

• Discriminant: b
2
– 4ac. Checking the value of the discriminant tells about the solutions:
• b
2
– 4ac > 0 indicates there are two real solutions.
• b
2
– 4ac = 0 indicates there is only one solution.
• b
2
– 4ac

Question 3

Analyzing the discriminant gives you an idea where to graph
the curve of a quadratic function.
Matching the graph with the elements of its function, this
parabola has:
· a value of a that is less than 0, because it turns down,
· a discriminant greater than 0 because it crosses the
x-axis twice and must have two real-number solutions.
This is a positive parabola with one real solution:
its a > 0 , and its discriminant = 0.
This is a positive parabola with two real solutions:
its a > 0, and its discriminant > 0.
This is a negative parabola with one real solution:
its a

Answer 3

Analyzing the discriminant gives you an idea where to graph
the curve of a quadratic function.
Matching the graph with the elements of its function, this
parabola has:
· a value of a that is less than 0, because it turns down,
· a discriminant greater than 0 because it crosses the
x-axis twice and must have two real-number solutions.
This is a positive parabola with one real solution:
its a > 0 , and its discriminant = 0.
This is a positive parabola with two real solutions:
its a > 0, and its discriminant > 0.
This is a negative parabola with one real solution:
its a