Q&A for How to Find the Maximum or Minimum Value of a Quadratic Function Easily

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How do you tell if a parabola is maximum or minimum?

Jake Adams
Academic Tutor & Test Prep Specialist
Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University.

Jake Adams

Academic Tutor & Test Prep Specialist

Expert Answer

First solve for a. If the value of a is a positive number, you'll have an upward-facing parabola and you'll need to find its minimum value. If a is a negative number, you'll have a downward-facing parabola and you'll need to find its maximum value.

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How do you tell if a parabola is up or down?

Jake Adams
Academic Tutor & Test Prep Specialist
Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University.

Jake Adams

Academic Tutor & Test Prep Specialist

Expert Answer

You can remember this concept by thinking about smiles and frowns. If someone is positive they smile, and if someone is negative, they frown. Similarly, a positive number will have an upward-facing parabola, and a negative number will have a downward-facing parabola.

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Question

How do I graph a quadratic function?

Community Answer

First, create a data table with multiple experimental values for x. Sub in those x coordinates and get y coordinates. Plot these along the x and y axis and join the dots with a smooth curve.

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After the value of y is found, how do we find the corresponding value of x?

Community Answer

Substitute the value of y found into the original(given) equation and solve for x.

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What are prerequisite skills for this topic?

Community Answer

A basic understanding of differentiation and how quadratic graphs work, as well as gradients, will be required before attempting this.

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What if the vertex form you have has no coefficient in the front of the parentheses?

Community Answer

You would need to rewrite the square in the equation in order to put it in vertex form.

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In the method four in example 1, why did he use c-b^2/2a? Why not 4a?

Community Answer

Because he was finding the minimum value. If he were finding max value, he would use 4a.

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What if the power is 3?

Donagan

Top Answerer

That's a cubic equation or function. See Solve a Cubic Equation .

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