Chapter 3: Linear and Quadratic Functions

<p>The line $x = h$ (C)</p> Signup and view all the answers

<p>By looking at the value of a (A)</p> Signup and view all the answers

<p>-(x - 2)(x - 4) (D)</p> Signup and view all the answers

<p>4 (C)</p> Signup and view all the answers

<p>The x-intercepts of the function (C)</p> Signup and view all the answers

<p>3x² + x - 6 (D)</p> Signup and view all the answers

<p>The point $(0, c)$ (A)</p> Signup and view all the answers

<p>The vertex is at (0.25, -0.5) (A)</p> Signup and view all the answers

<p>Completing the square (D)</p> Signup and view all the answers

<p>The vertex coordinates can be calculated from both forms. (D)</p> Signup and view all the answers

<p>(4, -2) (C)</p> Signup and view all the answers

<p>The parabola opens downwards (D)</p> Signup and view all the answers

<p>(0, -4) (B)</p> Signup and view all the answers

The point where the parabola intersects the y-axis. This point is also where x=0.

The highest or lowest point of a parabola. It is located halfway between the x-intercepts.

A function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

The form of a quadratic function written as f(x) = a(x - h)^2 + k. Where (h,k) is the vertex of the parabola, and a determines its shape.

The form of a quadratic function written as f(x) = a(x - r)(x - s). 'r' and 's' represent the x-intercepts of the parabola.

The form of a quadratic function written as f(x) = ax^2 + bx + c.

The point or points where the parabola intersects the x-axis, where y=0.

Transforming the equation of a quadratic function from one form to another, such as from vertex form to general form.

The vertex form of a quadratic function is written as f(x) = a(x - h)² + k where 'a', 'h', and 'k' are real numbers and 'a' cannot be zero. The 'h' and 'k' values represent the coordinates of the vertex (h, k).

In the vertex form, f(x) = a(x - h)² + k, the equation of the axis of symmetry is x = h, which is the vertical line passing through the vertex.

The parabola represented by the vertex form, f(x) = a(x - h)² + k, opens upwards if 'a' is positive and downwards if 'a' is negative.

The general form of a quadratic function is written as f(x) = ax² + bx + c, where 'a', 'b', and 'c' are real numbers and 'a' cannot be zero.

The x-coordinate of the vertex in the general form, f(x) = ax² + bx + c, is given by -b/(2a).

The y-intercept of the general form, f(x) = ax² + bx + c, is the point (0, c).

The factorized form of a quadratic function is written as f(x) = a(x - p)(x - q), where 'a', 'p', and 'q' are real numbers and 'a' cannot be zero. 'p' and 'q' represent the x-intercepts of the parabola.

In the factorized form, f(x) = a(x - p)(x - q), the equation of the axis of symmetry is x = (p + q)/2. It is the line that divides the parabola into two symmetrical halves.