After this lesson, you will be able to:
The student will be able to: Rewrite a quadratic function in vertex form using completing the square Find the vertex of a quadratic function Find x-intercepts and y-intercepts of a quadratic function Write a quadratic function given two points Solve a word problem involving a quadratic function Determine how a function has been transformed given an equation or a graph Given a description of a transformed function, write the equation of the new function.
Given the function below find the vertex, x-intercepts, and y-intercepts: Find a function whose graph is a parabola with vertex -2, -9 and that passes through the point -1, The profit function for a computer company is given by where x is the number of units produced in thousands and the profit is in thousand of dollars.
Determine how many thousands of units must be produced to yield maximum profit. Determine the maximum profit. Determine how many units should be produced for a profit of at least 40 thousand dollars. The graph of the function can be obtained from the graph of f x by what transformation?
Givenafter performing the following transformations:Let's look at one more example. Write the quadratic function for the graph that passes through the points (-1,0), (0,-1), and (1,0), where (0,-1) is the vertex. Reading through this problem, we see that we are given three points and it also tells us that -1 is the vertex.
Hmmm we can actually use either method. Write f(x) = 2x^2 - 4x + 7 in vertex form. √8, 2 real solutions, 0 imaginary solutions Find the discriminant of the related quadratic function and determine the number of real and imaginary solutions of 2y^2 - .
A line goes through the points (-1, 6) and (5, 4).
What is the equation of the line? Let's just try to visualize this.
So that is my x axis. And you don't have to draw it to do this problem but it always help to visualize That is my y axis. We'll write the general form of the quadratic: ax^2 + bx + c = y.
If the graph passes through the given points, that means that the coordinates of the points verify the equation of the quadratic. Because the vertex appears in the standard form of the quadratic function, The path passes through the origin and has vertex at For the following exercises, use the table of values that represent points on the graph of a quadratic function.
By determining the vertex and axis of symmetry, find the general form of the equation of the. A function is an equation that has only one answer for y for every x.
A function assigns exactly one output to each input of a specified type. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.