Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does 'a' represent in a quadratic equation?

Back

'a' is the coefficient of x² in the quadratic equation ax² + bx + c = 0. It determines the direction and width of the parabola.

Tags

CCSS.HSF-IF.C.7A

Front

What does 'b' represent in a quadratic equation?

Back

'b' is the coefficient of x in the quadratic equation ax² + bx + c = 0. It affects the position of the vertex of the parabola.

Front

What does 'c' represent in a quadratic equation?

Back

'c' is the constant term in the quadratic equation ax² + bx + c = 0. It represents the y-intercept of the parabola.

Tags

CCSS.HSF-IF.C.7A

Front

How do you identify the vertex of a parabola given by a quadratic equation?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the discriminant in the context of the Quadratic Formula?

Back

The discriminant is the part of the Quadratic Formula under the square root: b² - 4ac. It 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 roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

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 roots, but two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

Solve using the Quadratic Formula: 2x² + 17x + 21 = 0

Back

x = -7, x = -3/2.

Tags

CCSS.HSA-REI.B.4B