Good day students welcome to mathgotserved.com in this clip where going to be going over how to graph quadratic transformations so the instructions are as follows we are to write the equation of the quadratic function with the given information and graph it so for problem one we have equal genetic function that is stretched by a factor of two shifted three units to the left seen it's up and reflected downwards across the X axis aright will going to start by writing down the transformational form of or genetic functions okay so it's given by why equals plus or minus a timelines plus or minus the times X minor so plus H equals that pulls of brackets square plus or minus K okay so this is the transformational form of the Drabek function now how do we know that this function applies to the quadratic family while it is because we have to as an exponent okay it is of the form Y equals X squared so that's how we know that this is a function of the exponential from the exponential family okay now what we're going to do is assemble pieces of information from this paragraph and uses to generate the equation of the function with this description it is as though we are putting together pieces of the puzzle so let's start with the first piece of information it stretched horizontally by a factor of two so let's write that down stretched horizontally by a factor of two so what does that mean well if we're looking at the horizontal violation stats the role of be okay a our causes the graph to be direly tad stressed a compressed in the vertical direction so let's put some indicators here this goes dilates and reflects vertically and b dilates and reflects horizontally okay so in this case is we have a stretch by a factor of two we are going to have the absolute value of be equal to two right and if order righted it of the function we have and we have why equals two times X quantity T-square okay so this form just basically indicates that the quadratic function is this stretched horizontally by a factor of two right let's take a look at the next piece of information this has to do with Tom the shifts we're told that we're going to shift the current quadratic function three units to the left okay so what does this piece of information Tullis Lalitha of those that we have a situation where H is equal to -3 okay and we have a quadratic of the form Y equals quantity X +3 square remember H always goes in the reverse direction okay so when you writing it in its transformational form use opposite side so that's how you have it in there we're also told that we are shifting the quadratic two units up after she finished three units to the left so what does this tell us that those is that K is equal to two and we have the quadratic of the form Y equals X square +2 okay this represents the shifts two units in the upward direction now let's take a look at the last piece of information were provided with that can help us to generate the equation of the function with this description and that has to do with the reflection so we're told that the parabola below the crew Drabek function is reflected downwards across the x-axis so what does that tell us that tells us that a is going to be negative anytime you have the reflection of a or B or negative depending on the direction you're reflecting vertically in the direction of the x-axis is going to be negative if you're reflecting horizontally the direction of the Y axis then be will be negative so what we are going to do now is assemble these functions oh and we have and the have a quadratic of the form Y equals negative X square okay so this basically indicates the reflection of the prevalent in the direction of the X axis so that put all this together into the transformational form here to generate the equation of the problem so that you have why equals now a is negative but what about this magnitude of that number 80 there is no indication of it dilation in the vertical direction so that automatically means that a is equal to one okay if there is no dilation and direction of the a that makes a one of this will dilation in the direction of the be MXP one okay but in this problem we know that he was stretched the function was stretched by a factor of two has be is equal to two Ionescu altogether we now have a is -1 so have negative and that place there -1 of [be is going to be two dozen reflection in the horizontal direction Sobey's enemy positive to times X we have a shifts three units to the left +3 equals that and that we close the square components of our quadratic function and we have the two units upward shifts +2 okay so this is the quadratic function that has the information that was provided earlier here so what will do next is graft dysfunction okay with autographed these are prevalent function reflecting trying to show the transformation to happen okay so let's go ahead and set up our coordinate system have our y-axis in our X axis okay so when we are graph in a quadratic
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