Quadratic Functions: Forms, Graphing, and Transformations

A vocabulary flashcard deck covering quadratic function forms, axes of symmetry, vertices, domain and range, and conversions to vertex form.

Parent Function (Quadratic)

The most basic quadratic function, given by the equation $f(x) = x^2$.

Standard Form (Quadratic)

A quadratic function written in the form $f(x) = ax^2 + bx + c$.

Vertex Form (Quadratic)

A quadratic function written in the form $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex.

Axis of Symmetry Formula

The vertical line passing through the vertex of a parabola in standard form, given by the formula $x = \frac{-b}{2a}$.

Axis of Symmetry of $f(x) = -x^2 + 10x - 17$

The vertical line given by the equation $x = 5$, found using $x = \frac{-10}{2(-1)}$.

Vertex of $f(x) = -x^2 + 10x - 17$

The coordinate point $(5, 8)$, calculated by evaluating $f(5)$.

Range of $f(x) = -x^2 + 10x - 17$

The set of all possible dependent values: $\{y \mid y \le 8\}$.

Vertex of $f(x) = 2x^2 + 8x + 2$

The coordinate point $(-2, -6)$, found by evaluating $f(-2)$.

Range of $f(x) = 2x^2 + 8x + 2$

The set of all possible dependent values: $\{y \mid y \ge -6\}$.

Vertex of $f(x) = x^2 - 6$

The coordinate point $(0, -6)$, with an axis of symmetry at $x = 0$.

Vertex of $f(x) = (x + 4)^2 - 5$

The coordinate point $(-4, -5)$, identified directly from vertex form $(h, k)$.

Axis of Symmetry of $f(x) = -\frac{1}{2}(x + 3)^2$

The vertical line given by the equation $x = -3$.

Vertex of $f(x) = -\frac{1}{2}(x + 3)^2$

The coordinate point $(-3, 0)$.

Range of $f(x) = -\frac{1}{2}(x + 3)^2$

The set of all possible dependent values: $\{y \mid y \le 0\}$.

Transformed Quadratic Function (Vertical Stretch of 2, 5 Right, 1 Down)

The quadratic function written in vertex form as $f(x) = 2(x - 5)^2 - 1$.

Vertex Form of $f(x) = x^2 - 16x + 64$

The perfect square trinomial rewritten in vertex form as $f(x) = (x - 8)^2$.

Vertex Form of $f(x) = x^2 + 4x - 5$

The function rewritten by completing the square as $f(x) = (x + 2)^2 - 9$.

Vertex Form of $f(x) = -3x^2 + 6x + 4$

The function rewritten by completing the square as $f(x) = -3(x - 1)^2 + 7$.