WU Solve Quadratics

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

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, meaning they make the equation equal to zero.

Front

How can you determine the number of real roots a quadratic equation has?

Back

You can determine the number of real roots using the discriminant (D = b² - 4ac). If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean for a quadratic equation to be factorable?

Back

A quadratic equation is factorable if it can be expressed as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots.

Front

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

Back

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

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 equation x = -b/(2a).

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x, allowing you to express the equation in the form (x - p)² = q.

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola's opening: if a > 0, it opens upwards; if a < 0, it opens downwards.

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 (r1 + r2) is -b/a and the product of the roots (r1 * r2) is c/a.