Factored Form Quadratics

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How do you find the x-intercepts of a quadratic equation in factored form?

Back

Set the equation to zero and solve for x: (x - p)(x - q) = 0 leads to x = p and x = q.

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 images, given by the formula x = (p + q) / 2.

Front

How do you determine the vertex of a parabola from its factored form?

Back

The vertex can be found using the axis of symmetry and substituting it back into the equation to find the y-coordinate.

Front

What are the x-intercepts of the quadratic equation (x - 3)(x + 2) = 0?

Back

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

Front

What does the 'a' value in the factored form y = a(x - p)(x - q) indicate?

Back

The 'a' value indicates the direction and width of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

How can you convert a quadratic equation from standard form to factored form?

Back

Use factoring techniques such as grouping, or apply the quadratic formula to find the roots and express it in factored form.

Front

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

Back

The roots (or x-intercepts) are the points where the graph intersects the x-axis, indicating the solutions to the equation.

Front

How do you verify if a quadratic equation is correctly factored?

Back

Expand the factored form and check if it matches the original quadratic equation.

Front

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

Back

For a quadratic in the form y = ax^2 + bx + c, the sum of the roots is -b/a and the product of the roots is c/a.