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Graphing Parabolas

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Videos, worksheets, games and activities to help Algebra students learn how to graph parabolas that are written in the vertex form, y = a(x - h)2 + k, by using the coordinates (h, k) to graph the vertex.

What is the vertex form of a parabola?
The vertex form of a parabola is y = a(x - h)2 + k.

How to graph parabolas that are written in the vertex form?
Given the vertex form y = a(x - h)2 + k
1. Plot the vertex (h, k)
2. If a > 0 then (h, k) is the minimum point, if a < 0 then (h, k) is the maximum point.
3. Substitute x = 0, to get the y-intercept
4. Substitute y = 0, to get the x-intercept

How to convert a parabola from standard form to vertex form?
Short cut method:
Given a parabola, y = ax2 + bx + c,
1. Calculate \(h = - \frac{b}{{2a}},k = f\left( { - \frac{b}{{2a}}} \right)\)
2. Rewrite the equation as y = a(x - h)2 + k.

Graphing Parabolas in the vertex form y = a(x-h)2 + k
An animated video about graphing quadratic functions.
Graph parabola vertex form

How to Graph a Parabola
This is a quick review of all the parameters involved in graphing a problem in Vertex form.
Parabola Equations - Graphing Parabolas
Students learn to graph quadratic equations that are written in y - k = a(x - h)2 form by using the coordinates (h, k) to graph the vertex, and using the x and y-intercepts to graph the parabola. Students are reminded that to find the y-intercept, they must substitute a 0 in for x, and to find the x-intercept(s), they must substitute a zero in for y.


You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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