Front

What is the X-method for factoring quadratics?

Back

The X-method involves creating an 'X' where the top represents the product of the leading coefficient and the constant term, and the bottom represents the middle coefficient. You find two numbers that multiply to the top and add to the bottom, then use these to factor the quadratic.

Front

Factor the quadratic: 45x^2 - 80.

Back

5(3x - 4)(3x + 4)

Tags

CCSS.HSA.APR.C.4

Front

What are the roots of the quadratic equation x^2 + 2x = 12?

Back

x = -1 + \sqrt{13}, x = -1 - \sqrt{13}

Tags

CCSS.HSA-REI.B.4B

Front

How do you simplify the radical \sqrt{-117}?

Back

3i\sqrt{13}

Front

Solve by factoring: 4x^2 + 2x = 12.

Back

2(2x - 3)(x + 2)

Tags

CCSS.HSA-REI.B.4B

Front

What is a quadratic equation?

Back

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

Front

What is the quadratic formula?

Back

The quadratic formula is x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}, used to find the roots of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a quadratic to be factored?

Back

Factoring a quadratic means expressing it as a product of its linear factors, typically in the form (px + q)(rx + s).

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 b^2 - 4ac. It determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What are the possible values of the discriminant?

Back

If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root; if it is negative, there are two complex roots.

Tags

CCSS.HSA-REI.B.4B