Solving Quadratic Equations by Factoring

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots. Then, set each factor equal to zero and solve for x.

Front

What are the solutions to the equation (x-3)(x+2)=0?

Back

The solutions are x = 3 and x = -2.

Front

What does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means the discriminant (b² - 4ac) is less than zero, indicating that the parabola does not intersect the x-axis.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots of the equation.

Front

Solve the equation z² - 18z + 81 = 0 by factoring.

Back

The solution is z = 9.

Front

What are the roots of the equation a² + 2a - 24 = 0?

Back

The roots are a = -6 and a = 4.

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.

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as the product of two binomials.

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.