Solving quadratics

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x + p)² = q, making it easier to 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 roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax² + bx + c = 0.

Front

What does it mean for a quadratic equation to have no real solutions?

Back

A quadratic equation has no real solutions when the discriminant (b² - 4ac) is less than zero, indicating that the parabola does not intersect the x-axis.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero; they are also known as the roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the solutions 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-image halves, given by the formula x = -b/(2a) for the quadratic equation ax² + bx + c.

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

How do you determine the direction of a parabola?

Back

The direction of a parabola opens upwards if the coefficient a is positive and downwards if a is negative in the quadratic equation y = ax² + bx + c.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.