Graphing Parabolas Easily (All Types)

Complete guide to learning how to graph parabolas in the standard form, general form, vertex form, intercept form and focus/directrix form in this free math video tutorial by Mario's Math Tutoring.

0:13 4 Different Parabola Equation Forms Covered in this Video
0:42 General Form of the Parabola y=ax^2 + bx + c
0:46 Example 1 Graphing y= -3x^2 + 6x + 1
0:54 Formula for Finding Vertex of Parabola in y=ax^2 + bx + c Form
2:14 How to Find and Draw the Axis of Symmetry
2:33 How to Find Additional Points on the Parabola
3:10 Identifying and Using the Parent Function to Graph Points
4:40 How to Identify Whether the Parabola Opens Up or Down
4:51 Example 2 Graphing y=2x^2+8x+6
6:46 How to Identify Whether the Graph has a Max or Min Value
7:02 Equation of the Axis of Symmetry
7:10 How to Identify the Domain and Range of the Graph
7:50 Intercept Form of the Parabola (Factored Form)
8:06 How to Find the X-Intercepts
8:13 Example 1 Graph y=-1(x-3)(x-5)
9:01 How to Find the Axis of Symmetry and x-Coordinate of Vertex
9:15 Formula for Finding the Axis of Symmetry and x-Coordinate
11:25 Example 2 Graph y=2(x+2)(x-2)
13:38 Finding Domain and Range
13:53 Vertex Form of the Parabola y=a(x-h)^2 + k
14:37 Example 1 Graph y=-3(x-1)^2 + 6
16:24 Example 2 Graph y=4(x-2)^2 - 5
17:47 x^2=4py or y^2=4px or (x-h)^2=4p(y-k) or y^2=4p(x-h)
18:52 Discussing the Focus and Directrix and Parabola Definition
19:41 Example 1 Graph x^2=12y
19:52 Finding the "p" value or Distance From Vertex to Focus
20:00 Identifying the Vertex
20:09 How to Know if the Parabola Opens Up, Down, Left or Right
21:03 Using the Focal Chord 4p to Find Width of the Parabola
21:59 Example 2 Graph y^2=16x
23:59 Example 3 Graph (x-2)^2=4(y+1)

Related Videos:

Graphing Parabolas in General Form y=ax^2 +bx + c

Graphing Parabolas in Intercept Form y=a(x-p)(x-q)

Graphing Parabolas in Vertex Form y=a(x-h)^2 + k

Graphing Parabolas in Focus/Directrix Form x^2=4py or y^2=4px

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[avantikatewari]

This video was need to appreciated more. I've always had difficulty in understanding how to graph a parabola but now everything's clear!! Thanks a lot!!

[_rory]

standard form 0:12
Factored form 7:34
Vertex form 13:16

[nanyaverse]

11 days to the SAT and Mario explaining parabolas is what's keeping me sane

[valetinehilko]

16:20 You made a mistake. y = 4*x^2 and if x = 2, y = 8 (not 16 as in the video)

[frelenemaepolinar]

Sir our teacher told us to find the vertex of c in the equation x=ay²+by+c when a is not equal to zero? How to do it??

[antoninaghidirmic]

No doubt Mario masters the material and his explanations are very clear, with just one observation: do not talk so fast. Thank you!

[salmahassan]

Thank you so much for these videos they help a lot. I came from Algebra 1 Giant Review. At first I thought you spoke too fast and i sort of missed most things but everything was all good once i played the audio speed at 0.75. Thank you once again.

[suripatel]

Thank you Mario you are helping me not fail I love your videos

[vishnuteja]

Sir please make videos on straight lines...