Maximum or Minimum Value of Quadratic Equation Calculator

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Quadratic Equation

✖Numerical Coefficient a of Quadratic Equation is a constant multiplier of the variables raised to the power two in a Quadratic Equation.ⓘ Numerical Coefficient a of Quadratic Equation [a]			+10% -10%
✖Numerical Coefficient c of Quadratic Equation is the constant term or a constant multiplier of the variables raised to the power zero in a Quadratic Equation.ⓘ Numerical Coefficient c of Quadratic Equation [c]			+10% -10%
✖Numerical Coefficient b of Quadratic Equation is a constant multiplier of the variables raised to the power one in a Quadratic Equation.ⓘ Numerical Coefficient b of Quadratic Equation [b]			+10% -10%

✖Maximum/Minimum Value of Quadratic Equation is the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively.ⓘ Maximum or Minimum Value of Quadratic Equation [f_(x)Max/Min]

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Maximum or Minimum Value of Quadratic Equation

Formula

`"f"_{"(x)Max/Min"} = ((4*"a"*"c")-("b"^2))/(4*"a")`

Example

`"-50"=((4*"2"*"-42")-(("8")^2))/(4*"2")`

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Maximum or Minimum Value of Quadratic Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum/Minimum Value of Quadratic Equation = ((4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)-(Numerical Coefficient b of Quadratic Equation^2))/(4*Numerical Coefficient a of Quadratic Equation)
f_(x)Max/Min = ((4*a*c)-(b^2))/(4*a)
This formula uses 4 Variables

Variables Used

Maximum/Minimum Value of Quadratic Equation - Maximum/Minimum Value of Quadratic Equation is the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively.
Numerical Coefficient a of Quadratic Equation - Numerical Coefficient a of Quadratic Equation is a constant multiplier of the variables raised to the power two in a Quadratic Equation.
Numerical Coefficient c of Quadratic Equation - Numerical Coefficient c of Quadratic Equation is the constant term or a constant multiplier of the variables raised to the power zero in a Quadratic Equation.
Numerical Coefficient b of Quadratic Equation - Numerical Coefficient b of Quadratic Equation is a constant multiplier of the variables raised to the power one in a Quadratic Equation.

STEP 1: Convert Input(s) to Base Unit

Numerical Coefficient a of Quadratic Equation: 2 --> No Conversion Required
Numerical Coefficient c of Quadratic Equation: -42 --> No Conversion Required
Numerical Coefficient b of Quadratic Equation: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_(x)Max/Min = ((4*a*c)-(b^2))/(4*a) --> ((4*2*(-42))-(8^2))/(4*2)

Evaluating ... ...

f_(x)Max/Min = -50

STEP 3: Convert Result to Output's Unit

-50 --> No Conversion Required

FINAL ANSWER

-50 <-- Maximum/Minimum Value of Quadratic Equation

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 17 Quadratic Equation Calculators

Second Root of Quadratic Equation

Go Second Root of Quadratic Equation = (-(Numerical Coefficient b of Quadratic Equation)-sqrt(Numerical Coefficient b of Quadratic Equation^2-4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

First Root of Quadratic Equation

Go First Root of Quadratic Equation = (-(Numerical Coefficient b of Quadratic Equation)+sqrt(Numerical Coefficient b of Quadratic Equation^2-4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

Value of Quadratic Equation

Go Value of Quadratic Equation = (Numerical Coefficient a of Quadratic Equation*Value of X of Quadratic Equation^2)+(Numerical Coefficient b of Quadratic Equation*Value of X of Quadratic Equation)+(Numerical Coefficient c of Quadratic Equation)

Maximum or Minimum Value of Quadratic Equation

Go Maximum/Minimum Value of Quadratic Equation = ((4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)-(Numerical Coefficient b of Quadratic Equation^2))/(4*Numerical Coefficient a of Quadratic Equation)

Numerical Coefficient 'b' of Quadratic Equation

Go Numerical Coefficient b of Quadratic Equation = sqrt(Discriminant of Quadratic Equation+(4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation))

Second Root of Quadratic Equation given Discriminant

Go Second Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation-sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

First Root of Quadratic Equation given Discriminant

Go First Root of Quadratic Equation = (-Numerical Coefficient b of Quadratic Equation+sqrt(Discriminant of Quadratic Equation))/(2*Numerical Coefficient a of Quadratic Equation)

Numerical Coefficient 'a' of Quadratic Equation

Go Numerical Coefficient a of Quadratic Equation = (Numerical Coefficient b of Quadratic Equation^2-Discriminant of Quadratic Equation)/(4*Numerical Coefficient c of Quadratic Equation)

Numerical Coefficient 'c' of Quadratic Equation

Go Numerical Coefficient c of Quadratic Equation = (Numerical Coefficient b of Quadratic Equation^2-Discriminant of Quadratic Equation)/(4*Numerical Coefficient a of Quadratic Equation)

Discriminant of Quadratic Equation

Go Discriminant of Quadratic Equation = (Numerical Coefficient b of Quadratic Equation^2)-(4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)

Difference of Roots of Quadratic Equation

Go Difference of Roots of Quadratic Equation = sqrt(Discriminant of Quadratic Equation)/Numerical Coefficient a of Quadratic Equation

Value of X for Maximum or Minimum Value of Quadratic Equation

Go Value of X for Maximum/Minimum Value of f(X) = -Numerical Coefficient b of Quadratic Equation/(2*Numerical Coefficient a of Quadratic Equation)

Maximum or Minimum Value of Quadratic Equation using Discriminant

Go Maximum/Minimum Value of Quadratic Equation = -Discriminant of Quadratic Equation/(4*Numerical Coefficient a of Quadratic Equation)

Product of Roots of Quadratic Equation

Go Product of Roots = Numerical Coefficient c of Quadratic Equation/Numerical Coefficient a of Quadratic Equation

Sum of Roots of Quadratic Equation

Go Sum of Roots = -Numerical Coefficient b of Quadratic Equation/Numerical Coefficient a of Quadratic Equation

Product of Roots of Quadratic Equation given Roots

Go Product of Roots = First Root of Quadratic Equation*Second Root of Quadratic Equation

Sum of Roots of Quadratic Equation given Roots

Go Sum of Roots = (First Root of Quadratic Equation)+(Second Root of Quadratic Equation)

Maximum or Minimum Value of Quadratic Equation Formula

What is a Quadratic Equation?

A Quadratic Equation is an algebraic equation in some variable x with the highest degree of terms being 2. The Quadratic Equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a Quadratic Equation is the coefficient of x2 is a non-zero term(a ≠ 0). If the discriminant is positive, then the Quadratic Equation will have two real roots. If the discriminant is zero, then the Quadratic Equation will have one real root. If the discriminant is negative, then the Quadratic Equation will not have any real roots.

How to Calculate Maximum or Minimum Value of Quadratic Equation?

Maximum or Minimum Value of Quadratic Equation calculator uses Maximum/Minimum Value of Quadratic Equation = ((4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)-(Numerical Coefficient b of Quadratic Equation^2))/(4*Numerical Coefficient a of Quadratic Equation) to calculate the Maximum/Minimum Value of Quadratic Equation, The Maximum or Minimum Value of Quadratic Equation formula is defined as the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively. Maximum/Minimum Value of Quadratic Equation is denoted by f_(x)Max/Min symbol.

How to calculate Maximum or Minimum Value of Quadratic Equation using this online calculator? To use this online calculator for Maximum or Minimum Value of Quadratic Equation, enter Numerical Coefficient a of Quadratic Equation (a), Numerical Coefficient c of Quadratic Equation (c) & Numerical Coefficient b of Quadratic Equation (b) and hit the calculate button. Here is how the Maximum or Minimum Value of Quadratic Equation calculation can be explained with given input values -> -50 = ((4*2*(-42))-(8^2))/(4*2).

FAQ

What is Maximum or Minimum Value of Quadratic Equation?

The Maximum or Minimum Value of Quadratic Equation formula is defined as the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively and is represented as f_(x)Max/Min = ((4*a*c)-(b^2))/(4*a) or Maximum/Minimum Value of Quadratic Equation = ((4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)-(Numerical Coefficient b of Quadratic Equation^2))/(4*Numerical Coefficient a of Quadratic Equation). Numerical Coefficient a of Quadratic Equation is a constant multiplier of the variables raised to the power two in a Quadratic Equation, Numerical Coefficient c of Quadratic Equation is the constant term or a constant multiplier of the variables raised to the power zero in a Quadratic Equation & Numerical Coefficient b of Quadratic Equation is a constant multiplier of the variables raised to the power one in a Quadratic Equation.

How to calculate Maximum or Minimum Value of Quadratic Equation?

The Maximum or Minimum Value of Quadratic Equation formula is defined as the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively is calculated using Maximum/Minimum Value of Quadratic Equation = ((4*Numerical Coefficient a of Quadratic Equation*Numerical Coefficient c of Quadratic Equation)-(Numerical Coefficient b of Quadratic Equation^2))/(4*Numerical Coefficient a of Quadratic Equation). To calculate Maximum or Minimum Value of Quadratic Equation, you need Numerical Coefficient a of Quadratic Equation (a), Numerical Coefficient c of Quadratic Equation (c) & Numerical Coefficient b of Quadratic Equation (b). With our tool, you need to enter the respective value for Numerical Coefficient a of Quadratic Equation, Numerical Coefficient c of Quadratic Equation & Numerical Coefficient b of Quadratic Equation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum/Minimum Value of Quadratic Equation?

In this formula, Maximum/Minimum Value of Quadratic Equation uses Numerical Coefficient a of Quadratic Equation, Numerical Coefficient c of Quadratic Equation & Numerical Coefficient b of Quadratic Equation. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum/Minimum Value of Quadratic Equation = -Discriminant of Quadratic Equation/(4*Numerical Coefficient a of Quadratic Equation)

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