Solving quadratics

Front

What is a quadratic equation?

Back

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

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 are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of its linear factors.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you apply the zero product property to solve (x - 9)(x + 3) = 0?

Back

Set each factor equal to zero: x - 9 = 0 or x + 3 = 0, which gives x = 9 or x = -3.

Front

What are the roots or zeros of a quadratic equation?

Back

The roots or zeros of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you find the zeros of the quadratic equation x² - 9x + 20 = 0?

Back

Factor the equation to (x - 4)(x - 5) = 0, then set each factor to zero: x - 4 = 0 or x - 5 = 0, giving x = 4 and x = 5.

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.

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 two complex roots.