Quadratic Characteristics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find the y-coordinate.

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 are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, also known as the x-intercepts of the graph.

Front

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

Back

The number of roots can be determined using the discriminant (D = b² - 4ac): if D > 0, there are 2 real roots; if D = 0, there is 1 real root; if D < 0, there are no real roots.

Front

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

Back

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

Front

What is the formula for the vertex of a parabola in vertex form?

Back

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

Front

What is the effect of changing the value of 'b' in a quadratic function?

Back

Changing the value of 'b' affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola.