Quadratic formula and discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What does a discriminant of zero indicate?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Tags

CCSS.HSA-REI.B.4B

Front

How do you calculate the discriminant for the equation 2x² + 3x - 5?

Back

The discriminant is calculated as b² - 4ac = (3)² - 4(2)(-5) = 9 + 40 = 49.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation ax² + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.

Tags

CCSS.HSA.APR.B.2