Let's Watch
You've learned how rewrite a quadratic function from standard form to vertex form. You can use the vertex form of the quadratic function to identify the key features of its graph. You can also compare the features of the transformed graph to those of the graph of the parent function.
In the video below, the instructor will demonstrate how to use the values of a, h, and k to transform the graph of a quadratic function. Pay close attention to how he utilizes the value of a to determine additional points that lie along the parabola.
You may want to follow along using the study guide from earlier in the lesson.
In example one, we should note that the vertex of the parabola is located at negative two, three. And with an a-value of one, the parabola is the same shape as the parent graph and opens up (silent). In example two, we should note that the vertex of the parabola is located at three, negative one. And with an a-value of negative two, the graph is two times as tall as our parent function, and opens down. I hope this video helps you to graph your quadratic functions. Good luck!
In the video, the instructor first created the graph of \( f\left( x \right) = {(x + 2)}^{2} + 3 \). Compare the features of this transformed graph to the features of the graph of the parent function, \( g\left( x \right) = x^{2} \).
In the video, the instructor also created the graph of \( f\left( x \right) = {- 2(x - 3)}^{2} - 1 \). Compare the features of this transformed graph to the features of the graph of the parent function, \( g\left( x \right) = x^{2} \).
| Your Responses | Sample Answers |
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The parent function has a vertex at (0, 0). The graph of f(x) has a vertex at (\( - \)2, 3). Both the parent function and the graph of f(x) open up, and they are the same height. |
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The parent function has a vertex at (0, 0). The graph of f(x) has a vertex at (3, \( - \)1). The graph of the parent function opens up while the graph of f(x) opens down. The graph of f(x) stretches taller than the graph of the parent function. |
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