Review of Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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 can be found by factoring, using the quadratic formula, or completing the square.

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. It passes through the vertex of the parabola and is given by the formula x = -b/(2a).

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it means that the coefficient 'a' in the equation y = ax² + bx + c is positive. This indicates that the vertex is a minimum point.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, it means that the coefficient 'a' in the equation y = ax² + bx + c is negative. This indicates that the vertex is a maximum point.

Front

What is the quadratic formula?

Back

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

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 b² - 4ac. It determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How do you determine if a quadratic has a maximum or minimum value?

Back

To determine if a quadratic has a maximum or minimum value, check the sign of 'a': if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the vertex form of a quadratic function?

Back

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