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

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 + 4)(x - 3) = 0?

Back

Set each factor equal to zero: x + 4 = 0 or x - 3 = 0. This gives the solutions x = -4 and x = 3.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Apply the Zero-Product Property. 4. Solve for x.

Front

What are the roots of the equation 3x² + 9x - 30 = 0?

Back

The roots are x = 2 and x = -5.

Front

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

Back

To find the roots, factor the quadratic equation into the form (x - p)(x - q) = 0, then solve for x by setting each factor to zero.

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.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and can be found using the formula x = -b/(2a).

Front

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

Back

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