Quadratic Equation Exercises
About Quadratic Function
Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. The standard form is useful for determining how the graph is transformed from the graph of latexyx2latex. The figure below is the graph of this basic function.
Another method involves starting with the basic graph of 92fxx292 and 'moving' it according to information given in the function equation. We call this graphing quadratic functions using transformations. In the first example, we will graph the quadratic function 92fxx292 by plotting points.
Section 2.1 Transformations of Quadratic Functions 51 Writing a Transformed Quadratic Function Let the graph of g be a translation 3 units right and 2 units up, followed by a refl ection in the y-axis of the graph of fx x2 5x.Write a rule for g. SOLUTION Step 1 First write a function h that represents the translation of f. hx fx 3 2 Subtract 3 from the input.
A quadratic function's graph is a u-shape curve known as the parabola. There are 4 transformations that may happen to a quadratic function translation or shifting that will move it horizontally
Graph Quadratic Functions Using Transformations In the following exercises, rewrite each function in the f x a x h 2 k f x a x h 2 k form by completing the square. 325 .
Transforming Quadratic Functions. This is the graph of y x 2 This is the graph of y x 2 that has undergone transformations The vertex of the red parabola has been shifted to 3, 1 and note that the sides of the parabola open upward but they appear steeper and longer than those on the blue parabola.
A transformation of a quadratic equation is an operation happening to the initial function fx that changes the function in some way 1 Expression 2 quotfquot left parenthesis, quotxquot , right parenthesis equals quotxquot squared f x x 2
Types of Transformations 1. Vertical Transformations Transformation Formula What to do to the Coordinates Vertical shift up c Vertical shift down c Vertical stretch Vertical shrink Re ection about the x-axis Example. Consider the quadratic function fx x2. A vertical shift up by 3 transforms the function to fx 3 x2 3. 2 2 2 4 6
Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. The standard form is useful for determining how the graph is transformed from the graph of latexyx2latex. The figure below is the graph of this basic function.
Day 1 Quadratic Transformations A parent function is the simplest function of a family of functions. For the family of quadratic functions, y ax2 bx c, the simplest function of this form is y x2.or fx 2 x There are several different forms a quadratic function can be written in, but the one we are going to work with
