Q&A for How to Graph a Parabola

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How do I actually draw the parabola?

Elena Himmerich

Community Answer

Draw a smooth line through the points you've graphed. Keep in mind the U-shape of the parabola. Put arrows at the ends.

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Question

How do I draw a graph with the function f(x) = -4x^2 + 32?

Donagan

Top Answerer

This is no different from any other parabola. Make a two-column table. Choose convenient values for x. Calculate the corresponding values for y or f(x). Plot the paired-value points on a grid. Connect the points.

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Question

How do I find the formula for a given parabola?

Donagan

Top Answerer

It's not possible simply to view a parabola and deduce its equation. If a parabola is "given," that implies that its equation is provided.

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If the axis of symmetry is anything other than 0, how do you make the table?

Linnie

Top Answerer

The axis of symmetry doesn't need to be 0 for you to make a table. To make a table, simply choose a value for x, such as 0, and plug it into the original equation to solve for y. Record the value of y, and that gives you a point to use when graphing the parabola.

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Question

How to widen the parabola (arms)? I am making a lamp reflector. Does the coefficient of x become less than one to achieve this widening?

ARandomWikilover77

Community Answer

To widen the parabola, simply modify the value of “a”, as this has an influence on the width of the parabola. I believe “b”, which can influence the axis of symmetry, also interacts with intensity. This is because they are multiplied with “x” to provide a larger or smaller value to “y”, and this is also why it can curve up or down depending on the positivity of the “a” coefficient.

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