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Course: Algebra 1 (Eureka Math/EngageNY)>Unit 4

Lesson 8: Topic A: Lessons 8-10: Parabolas intro

Parabolas intro

Graphs of quadratic functions all have the same shape which we call "parabola." All parabolas have shared characteristics. For example, they are all symmetric about a line that passes through their vertex. This video covers this and other basic facts about parabolas.

Want to join the conversation?

• does the parabolas ever "touch" and turn into an ellipse?
• I assume that you are talking about the lines of a parabola. If so, no. because then what you are looking at is not a parabola. It would be, as you said, an ellipse or circle.
• Does the opening upwards or opening downwards of a parabola depend on anything?
• After a month, finally got to unit 14 🥹
• I dunno, parabolas seem to be a bit more curved than very straight forward...
• What would the equation be for a Parabola that is sideways?
• x=y^2 would create a parabola that goes sideways. Note: it would not be a function.
• I'm here fixing what I missed in school but now I got to something we didn't even study yet I can only feel proud
• Why are they called "quadratics"?
• The Latin word for square is quadratum. Since the area of a square is the square of its side length, words similar to this are sometimes used to mean square, the operation. Quadratics are named thus because the function involves squaring the input.
• Is it possible to determine the magnitude of the curve of a parabola ?
Like line graphs have slopes which shows the magnitude of their slope-iness (i can't think of a better word :P ). So is there anything like that for parabolas ? And how do you find it ?
• Yes, by comparing it to the parent function, y = x^2. On a graph, the parent function has the vertex at the origin (0,0) and additional reflexive points (1,1) and (-1,1) because both (1)^2 and (-1)^2 equal 1, then (2,4) and (-2,4), (3,9) and (-3,9). So if we go over 1, we can see how much we go up to see the magnitude. If we start at the vertex (it does not matter where it is on the graph), go over 1 and count how much you go up or down to determine the magnitude. Several examples and for simplicity's sake, keep the vertex at the origin. If I go over one up two, then the equation is y = 2x^2. over 1 up 3 it is y = 3x^2, over 1 down 1, then y = - x^2, over 1 down 2, then y = -2x^2. It gets a little harder with fractions, but if I go over 2 up 2, then it is y = 1/2x^2 (compared to (2,4)) or over 2 up 1, then it is y = 1/4 x^2, over 2 down 3, then it is y = - 3/4 x^2, over 3 up 3, then it is y = 1/3 x^2.