Quadratics Models & transformations

Front

What is a quadratic function?

Back

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

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the function f(x) = ax^2 + bx + c.

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).

Front

How do transformations affect the graph of a quadratic function?

Back

Transformations such as translations, reflections, and stretches/compressions can change the position and shape of the graph. For example, f(x) = a(x-h)^2 + k translates the graph h units horizontally and k units vertically.

Front

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

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

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

Back

The maximum or minimum value occurs at the vertex of the parabola. If the parabola opens upwards, the vertex represents the minimum value; if it opens downwards, it represents the maximum value.

Front

How can you find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where the expression under the square root is called the discriminant.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula. It determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

Vertex form is expressed as f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola. This form makes it easy to identify the vertex and graph the function.