finding solutions to 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 are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called the roots or zeros of the equation.

Front

How can you find the roots of a quadratic equation?

Back

You can find the roots of a quadratic equation using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are two complex roots.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

The first step is to rearrange the equation to set it equal to zero by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

How do you factor the quadratic equation x² + 12x + 35 = 0?

Back

To factor the equation, look for two numbers that multiply to 35 and add to 12. The factors are (x + 5)(x + 7) = 0.

Front

What are the solutions to the quadratic equation x² + 2x - 15 = 0?

Back

The solutions are x = -5 and x = 3, found by factoring the equation as (x + 5)(x - 3) = 0.

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 find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for the variable.

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.