Quadratic Equations from Patterns

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 does the term 'vertex' refer to in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on whether it opens upwards or downwards.

Front

How can you identify the axis of symmetry in a quadratic equation?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax² + bx + c = 0.

Front

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

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you represent the area of a square in terms of its side length x?

Back

The area of a square is represented by the equation A = x², where A is the area and x is the length of one side.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax² + bx + c.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards when the coefficient 'a' in the equation ax² + bx + c is positive, indicating that the vertex is the minimum point.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards when the coefficient 'a' is negative, indicating that the vertex is the maximum point.

Front

How can you represent the area of a rectangle in terms of its length l and width w?

Back

The area of a rectangle is represented by the equation A = l * w.