SOLUTION: What is the maximum or minimum value of f(x)=2x^2-8x-3 and how do you find it?

Question 1108467: What is the maximum or minimum value of f(x)=2x^2-8x-3 and how do you find it?
Found 3 solutions by josgarithmetic, ikleyn, TeachMath:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
recognize the form of the equation and what is should mean. Leading coefficient on x^2 term is positive, so vertex of parabola, a minimum. This occurs exactly in the middle of the two roots, regardless of complex or real. Also if you want and know how, find derivative of f(x); rate of change is 0 at this minimum point.

-------what is ?

Minimum point is (2, -11).

You can also try to factorize f(x) to find the zeros.
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

Use the "completing the square method: 2x^2 - 8x - 3 = = (2x^2 - 8x + 8) - 8 - 3 = = 2*(x - 4x + 4) - 11 = = 2*(x-2)^2 - 11. The minimum is achieved at x= 2. The value of the minimum is -11.

Solved.

-----------------
See the lessons
    - HOW TO complete the square - Learning by examples

    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by TeachMath(96)   (Show Source): You can put this solution on YOUR website!
This will have a MINIMUM value since a > 0
The minimum value occurs where x = - b/2a, or at x = - - 8/(2 * 2), or at x =8/4, or at x = 2
Substitute 2 for x in equation to get: f(2) = 2(2)^2 - 8(2) - 3
f(2) = 8 - 16 - 3
f(2), or minimum value = - 11
RELATED QUESTIONS
Hi, Can you help me with this math problem? Find the maximum or minimum point (answered by checkley77)
Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by Earlsdon)
How do you find the standard form, vertex, line of symmetry, and maximum or minimum... (answered by ankor@dixie-net.com)
Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by lwsshak3)
Find the vertex, the line of symmetry, and the maximum or minimum value of f(x).... (answered by likaaka)
Find the vertex, the line of symmetry, and the maximum or minimum value of f(x).... (answered by ewatrrr)
Find the vertex of f(x) = x^2-10x+21. Is the vertex the maximum or minimum value of f?... (answered by Earlsdon)
f(x)=-2x^2+8x-12 does the function have a minimum or maximum value? where does the... (answered by MathLover1)
Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by solver91311)