Solving 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 means 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 solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, first set the equation to zero, factor it into two binomials, and then use the zero-product property to find the values of x.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, which correspond to the solutions of the equation when y = 0.

Front

What is the first step in solving x² - 9x = 10 by factoring?

Back

The first step is to rearrange the equation to set it to zero: x² - 9x - 10 = 0.

Front

How do you find the roots of the equation (x - 3)(x + 6) = 0?

Back

Set each factor equal to zero: x - 3 = 0 gives x = 3, and x + 6 = 0 gives x = -6.

Front

What is the significance of the coefficients in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

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

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).