Quadratic formula and discriminant

Front

What is the quadratic formula used to find the solutions of a quadratic equation?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the value of the discriminant for the equation x² + 4x + 4?

Back

The discriminant is zero, indicating that there is one real root.

Tags

CCSS.HSA-REI.B.4B

Front

How do you determine if a quadratic equation has real solutions?

Back

Calculate the discriminant (b² - 4ac). If it is greater than or equal to zero, the equation has real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the equation 0 = x² + 5x + 7?

Back

There are no real solutions because the discriminant is negative.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does it mean if the discriminant is positive?

Back

It means the quadratic equation has two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the coefficients a, b, and c in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

Tags

CCSS.HSF-IF.C.7A

Front

How can you solve a quadratic equation using factoring?

Back

Set the equation to zero, factor it into two binomials, and then set each factor equal to zero to find the solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.