Solving Quadratic Equations using Any Method

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 is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b² - 4ac. It determines the nature of the roots of the equation.

Front

How do you determine the number of real solutions using the discriminant?

Back

If the discriminant (D) is greater than 0, there are two distinct real solutions. If D equals 0, there is one real solution (a repeated root). If D is less than 0, there are no real solutions.

Front

What are the solutions to the equation 2x² + 3x + 1 = 0?

Back

Using the quadratic formula, the solutions are x = -1 and x = -0.5.

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

How can you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h), where f(h) is the value of the function at 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

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

Back

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