SOLUTION: For the following function, find the vertex and the maximun or min value: h(x)=-2x^2+6x-3 so far I have done is -2(x^2-3x)-3 I'm not sure if I am suppose to find the per

Question 22027: For the following function, find the vertex and the maximun or min value:
h(x)=-2x^2+6x-3

so far I have done is -2(x^2-3x)-3
I'm not sure if I am suppose to find the perfect square or what.
Thanks for your help.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
h(x)=-2x^2+6x-3

so far I have done is -2(x^2-3x)-3....OK
I'm not sure if I am suppose to find the perfect square ....YES DO IT ...YOU HAVE TO USE THE GIVEN X^2 AND X TERMS TO MAKE A PERFECT SQUARE
=-2(X^2-2*1.5*X+1.5^2-1.5^2)-3
=-2{X-1.5)^2-1.5^2}-3
=-2(X-1.5)^2+2*1.5*1.5-3
=-2(X-1.5)^2+1.5=Y SAY...Y=1.5-2(X-1.5)^2
NOW ,WE REASON OUT THAT (X-1.5)^2 BEING PERFECT SQUARE IT IS ALWAYS POSITIVE. SO ITS MIIMUM VALUE IS ZERO WHEN X=1.5
NOW WHEN THIS IS ZERO,Y WILL BECOME MAXIMUM SINCE WE ARE SUBTRACTING THE MINIMUM POSSIBLE VALUE FROM 1.5....YO Y HAS A MAXIMUM VALUE OR VERTEX AT X=1.5
RELATED QUESTIONS
Find [g*h](x) and [h*g](x) 12. g(x)=-2x H(x)= x^2+3x+2 So this is what I've... (answered by solver91311)

this is one question with different parts Find the vertex, line of symmetry, maximum or (answered by solver91311,MathLover1)

p(x)=-2x^2+39x-132 find the maximun and minimum i belive the vertex is... (answered by richard1234)

Quadratic Functions and Equations The first question I gave it go at. Solve.... (answered by richwmiller,solver91311)

how do i "rewrite this function in the form {{{y=(x-h)^2+k}}} by completing the square.... (answered by sabanasir)

1) Find the vertex, the line of symmetry, and the max or min value of f(x). Graph the... (answered by solver91311)

what are the vertex, focus and directrix of parabola 12y=x^2-6x+45? have so far:... (answered by lwsshak3)

Please check my work for max/min problem. Find the max/min of: f(x) = 2x^3 - 3x^2 + 6 (answered by Fombitz)

find the vertex, the line of symmetry, the max or min value of the quadratic function (answered by nerdybill)