SOLUTION: find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16

Question 155098: find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16
----------------------------------
Plot those points and you will see that f(-6) = 16 by symmetry about
the x-axis
-----------------
So you have three points: (-6,16),(-2,-16),(2,16)
----------------------------------------------------
Substitute these into ax^2 + bx + c = y
to get three equations with unknowns a,b, and c.
36a -6b + c = 16
4a -2b + c =-16
4a +2b + c = 16
-------------------------
Use any method to solve this system to get:
a = 2
b = 8
c =-8
---------------
EQUATION:
y = 2x^2 + 8x -8
==========================
Cheers,
Stan H.
RELATED QUESTIONS
Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by stanbon,solver91311)

Find the minimum value of the function f(x) = x^2 + 9x �... (answered by josgarithmetic,ikleyn,MathTherapy)

what is the equation of the quadratic function described of the minimum value of f is... (answered by scott8148)

What does it mean when it says "find the quadratic equation where f(1)=2 and the maximum... (answered by Fombitz)

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, the maximum or minimum value of the quadratic... (answered by Earlsdon)

The function f is such that f(x) = a - bcosx for 0° ≤ x ≤ 360°, where a and b are... (answered by math_tutor2020)

given f(x)=4x^2-1 /x^2-16 a. Find the x-intercept(s). b. Find the y-intercept(s).... (answered by stanbon)