Solving Quadratic Equations Review

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 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

How do you factor a quadratic equation?

Back

To factor a quadratic equation, you need to express it in the form (x - p)(x - q) = 0, where p and q are the roots of the equation.

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, given by b² - 4ac, indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x, allowing you to express it as a perfect square.

Front

What are the roots of the equation x² - 11x + 24 = 0?

Back

The roots are x = 3 and x = 8, found by factoring the equation as (x - 3)(x - 8) = 0.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in standard form, factor it into two binomials, and set each factor equal to zero to find the roots.

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

What is the significance of the coefficients a, b, and c in a quadratic equation?

Back

The coefficient a determines the direction and width of the parabola, b affects the position of the vertex, and c represents the y-intercept.