Different Forms of Quadratic Functions

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 does the coefficient 'a' in a quadratic function determine?

Back

The coefficient 'a' determines the direction in which the parabola opens: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

To find the vertex of a quadratic function in standard form f(x) = ax² + bx + c, use the formula h = -b/(2a) and then calculate k by substituting h back into the function.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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 = h, where h is the x-coordinate of the vertex.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, complete the square.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If 'a' is positive, the vertex represents a minimum; if 'a' is negative, it represents a maximum.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.