Solving quadratic Equations by completing the Squares

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Tags

CCSS.HSA-REI.B.4B

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the value of C in the equation x² + 24x + C?

Back

To find C, complete the square: C = (24/2)² = 144.

Tags

CCSS.HSA-REI.B.4B

Front

What are the roots of the quadratic equation x² - 8x + 12 = 0?

Back

The roots are x = 2 and x = 6, found by factoring the equation.

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 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, only complex roots.

Tags

CCSS.HSA-REI.B.4B