Algebra 2: Resources and Extra Practice - 2.04 Graphing Quadratics

Algebra 2: Resources and Extra Practice

2.04 Graphing Quadratics

Essential Question:

In what ways does adding a constant or coefficient to a quadratic equation affect the graph?
How are the axis of symmetry and vertex related?
What key features of a quadratic graph can be identified?

Lesson204.mp4

Lesson 2.04 Video - If video does not load correctly, Click Here to watch video.

Khan Academy Resources

Graphing quadratics: vertex formLearn how to graph any quadratic function that is given in vertex form. Here, Sal graphs y=-2(x-2)²+5.

Quadratic word problems (vertex form)Given a quadratic function that models the height of an object being launched from a platform, we analyze the function to answer questions like "what is the height of the platform?" or "when does the object reach its maximum height?"

Intro to parabola transformationsSal discusses how we can shift and scale the graph of a parabola to obtain any other parabola, and how this affects the equation of the parabola.

Shifting parabolasThe graph of y=(x-k)²+h is the resulting of shifting (or translating) the graph of y=x², k units to the right and h units up. For example, y=(x-3)²-4 is the result of shifting y=x² 3 units to the right and -4 units up, which is the same as 4 units down.

Scaling & reflecting parabolasThe graph of y=k⋅x² is the graph of y=x² scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of a parabola from its graph.

Graphing quadratics: standard formLearn how to graph any quadratic function that is given in standard form. Here, Sal graphs y=5x²-20x+15.

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