Key Quadratic Attributes

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 can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If the parabola opens upwards (a > 0), it has a minimum value; if it opens downwards (a < 0), it has a maximum value.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, located at the coordinates (h, k) in the vertex form of a quadratic equation: y = a(x - h)^2 + k.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value 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 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 can 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.

Front

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

Back

The discriminant (D = b^2 - 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 formula for the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex if the parabola opens downwards. It is the y-coordinate of the vertex.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex if the parabola opens upwards. It is the y-coordinate of the vertex.