##### Asked by: Mayo Pellegrino
science space and astronomy

# How do you find the maximum value of a quadratic function?

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If you are given the formula y = ax2 + bx + c, thenyoucan find the maximum value using the formula max =c- (b2 / 4a). If you have the equation y = a(x-h)2 + k and theaterm is negative, then the maximum value is k.

Keeping this in view, how do you find the minimum value of a quadratic equation?

If your quadratic equation has a positive aterm,it will also have a minimum value. You can findthisminimum value by graphing the function or by using oneofthe two equations. If you have the equation intheform of y = ax^2 + bx + c, then you can find theminimumvalue using the equation min = c -b^2/4a.

Furthermore, what is the maximum in math? Maximum, In mathematics, a point at whichafunction's value is greatest. If the value is greater than orequalto all other function values, it is an absolutemaximum. Ifit is merely greater than any nearby point, it isa relative, orlocal, maximum.

Thereof, what is the maximum value of a function?

The maximum value of a function is the placewherea function reaches its highest point, or vertex, on agraph.For instance, in this image, the maximum value ofthefunction is y equals 5. Practically, finding themaximumvalue of a function can be used to determinemaximumprofit or maximum area.

What is the maximum of a function?

A continuous function may assume amaximumat a single point or may have maxima at a number ofpoints. Aglobal maximum of a function is the largestvalue inthe entire range of the function, and a localmaximumis the largest value in some localneighborhood.

Explainer

## How do you find the range?

Summary: The range of a set of data isthedifference between the highest and lowest values in the set.Tofind the range, first order the data from least togreatest.Then subtract the smallest value from the largest value intheset.

Explainer

## What is local maximum and minimum of a graph?

Local minimum value of a function f (x) onagraph, is a value at a point (like Q in thegraph).Thus, f (Q) is the local minimum value of thefunction f(x). Global Maximum and Minimum Values : Globalmaximumand minimum values are also known as the absolutemaximumand minimum values.

Pundit

## How do you find the range of a parabola?

The values of a, b, and c determine the shapeandposition of the parabola. The domain of a function istheset of all real values of x that will give real values for y.Therange of a function is the set of all real values of ythatyou can get by plugging real numbers into x. The quadraticparentfunction is y = x2.

Pundit

## Where does the minimum or maximum value occur?

The minimum or maximum of a functionoccurswhen the slope is zero. Therefore, to find where theminimum ormaximum occurs, set the derivative equal tozero.

Pundit

## WHAT IS A in vertex form?

The vertex form of a quadratic is given by. y=a(x – h)2 + k, where (h, k) is thevertex.The "a" in the vertex form is the same "a" as.in y =ax2 + bx + c (that is, both a's have exactly thesamevalue). The sign on "a" tells you whether the quadratic opensup oropens down.

Pundit

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

The general form of the equation of a parabolais:Look at the coefficient of the term, that's the a, andIf a> 0 (positive), then the parabola opensupward and thegraph has a minimum at its vertex. Ifa < 0(negative), then the parabola opens downward andthe graphhas a maximum at its vertex.

Pundit

## What is a relative maximum and minimum?

A relative maximum or minimum isslightlydifferent. All that's required for a point to be arelativemaximum or minimum is for that point to beamaximum or minimum in some interval of x 'saroundx=c . This means that relative extrema do not occur attheend points of a domain.

Teacher

## How do I find the Y intercept of a parabola?

To find the y-intercept let x = 0 andsolvefor y. Step 3: Find the x-intercept(s).Tofind the x-intercept let y = 0 and solvefor x.You can solve for x by using the square root principle orthequadratic formula (if you simplify the problem intothecorrect form).

Teacher

## How do you find the vertex?

We find the vertex of a quadratic equation withthefollowing steps:
1. Get the equation in the form y = ax2 + bx + c.
2. Calculate -b / 2a. This is the x-coordinate of the vertex.
3. To find the y-coordinate of the vertex, simply plug the valueof-b / 2a into the equation for x and solve for y.

Teacher

## How do you find the domain?

For this type of function, the domain is allrealnumbers. A function with a fraction with a variable inthedenominator. To find the domain of this typeoffunction, set the bottom equal to zero and exclude the x valueyoufind when you solve the equation. A function with avariableinside a radical sign.

Teacher

## How do you graph a function?

Graphs of functions are graphsofequations that have been solved for y! The graph of f(x)inthis example is the graph of y = x2 - 3. Itiseasy to generate points on the graph. Choose a value forthefirst coordinate, then evaluate f at that number to find thesecondcoordinate.

Reviewer

## How do you graph parabolas?

If the leading coefficient is positive, thentheparabola opens upward. All quadratic equations of theformy=ax2+bx+c y = a x 2 + b x + c have parabolic graphswithy-intercept (0, c). However, not all parabolas havexintercepts. Example 3: Graph: y=2x2+4x+5 y = 2 x 2 + 4 x +5.

Reviewer

## How do you identify the domain and range of a function?

Another way to identify the domain and rangeoffunctions is by using graphs. Because thedomainrefers to the set of possible input values, thedomain of agraph consists of all the input values shown onthe x-axis. Therange is the set of possible output values,which are shownon the y-axis.

Reviewer

## How do you find a value in vertex form?

f (x) = a(x - h)2 + k, where (h, k) isthevertex of the parabola. FYI: Different textbookshavedifferent interpretations of the reference "standardform"of a quadratic function. Some say f (x) =ax2 + bx + cis "standard form", while others saythat f (x) = a(x -h)2 + k is "standardform".

Reviewer

## How do you factor a quadratic equation?

With the quadratic equation in this form:
1. Step 1: Find two numbers that multiply to give ac (inotherwords a times c), and add to give b.
2. Step 2: Rewrite the middle with those numbers:
3. Step 3: Factor the first two and last two termsseparately:

Supporter

## What is the axis of symmetry?

Axis of Symmetry of a Parabola. The graph ofaquadratic function is a parabola. The axis of symmetry ofaparabola is a vertical line that divides the parabola intotwocongruent halves. The axis of symmetry always passesthroughthe vertex of the parabola .

Supporter

## What is the discriminant of a quadratic equation?

Mathwords: Discriminant of a Quadratic. ThenumberD = b2 – 4ac determined from thecoefficients ofthe equation ax2 + bx + c = 0.Thediscriminant reveals what type of roots theequationhas.

Supporter

## What does the quadratic formula find?

The Quadratic Formula uses the "a", "b", and"c"from "ax2 + bx + c", where "a", "b", and "c" arejustnumbers; they are the "numerical coefficients" of thequadraticequation they've given you to solve.

Beginner

## How do you find the zeros of a function?

To see a basic example of this, considerthefunction f(x) = x + 1. If you set the functionequalto zero, then it will look like 0 = x + 1, which gives you x =-1once you subtract 1 from both sides. This means that the zeroofthe function is -1, since f(x) = (-1) + 1 gives you aresultof f(x) = 0.

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23rd June, 2020

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