Solve Quadratics by Factoring

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 does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation involves rewriting it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

How do you find the roots of a quadratic equation by factoring?

Back

To find the roots, set the factored form of the equation to zero and solve for x: (x - p)(x - q) = 0 leads to x = p or x = q.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots (p + q) is -b/a and the product of the roots (pq) is c/a.

Front

Solve the quadratic equation: 3x² + 9x - 30 = 0.

Back

x = 2, -5.

Front

Solve the quadratic equation: x² = 18x - 81.

Back

x = 9, 9.

Front

Solve the quadratic equation: x² - 7x = 0.

Back

x = 0, 7.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How can you determine if a quadratic has a maximum or minimum vertex?

Back

If the coefficient of x² (a) is positive, the parabola opens upwards and has a minimum vertex. If a is negative, it opens downwards and has a maximum vertex.

Front

What is the standard form of a quadratic equation?

Back

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