quadratic formula

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 does the 'a' value represent in a quadratic equation?

Back

The 'a' value represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Tags

CCSS.HSF-IF.C.7A

Front

What does the 'b' value represent in a quadratic equation?

Back

The 'b' value is the coefficient of x and affects the position of the vertex of the parabola along the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What does the 'c' value represent in a quadratic equation?

Back

The 'c' value is the constant term and represents the y-intercept of the quadratic function.

Tags

CCSS.HSF-IF.C.7A

Front

How do you identify the coefficients a, b, and c in the equation 4x² - 8x = 3?

Back

Rearranging the equation to standard form gives 4x² - 8x - 3 = 0, so a = 4, b = -8, c = -3.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots, but two complex roots.

Tags

CCSS.HSA-REI.B.4B