AFDA Test Review Quadratic Functions

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

Front

How do you find the axis of symmetry for 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 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 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.

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 transformations affect the graph of a quadratic function?

Back

Transformations such as translations, reflections, and stretches/compressions can change the position, orientation, and shape of the graph of a quadratic function.

Front

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

Back

Changing the value of 'a' affects the width and direction of the parabola: if |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider; if a < 0, the parabola opens downward.

Front

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

Back

The maximum or minimum value can be found at the vertex of the parabola, calculated using the vertex formula and substituting the x-coordinate back into the function.

Front

What is the relationship between the roots and the factors of a quadratic function?

Back

The roots of a quadratic function correspond to the values of x that make the function equal to zero, and they can be expressed as factors in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots.