2/24 Quadratic Patterns

Front

What is a quadratic relationship?

Back

A quadratic relationship is a type of mathematical relationship where the highest degree of the variable is 2, typically represented by the equation of the form y = ax^2 + bx + c, where a, b, and c are constants.

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 a quadratic function. It is the point where the graph changes direction.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the axis of symmetry in a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

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

Back

The coefficient 'a' determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the quadratic formula?

Back

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

Front

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

Back

The number of real roots can be determined by calculating the discriminant (b² - 4ac). If the discriminant is positive, there are two real roots; if it is zero, there is one real root; if it is negative, there are no real roots.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form y = ax^2 + bx + c.

Front

What does it mean for a quadratic function to be in vertex form?

Back

A quadratic function is in vertex form when it is expressed as y = a(x - h)² + k, where (h, k) is the vertex of the parabola.