f(x)=-2x^2+5x-8 in standard from

Question

Advanced functions math

Answer 1

The general form of a quadratic equation is f(x)=ax²+bx+c 

 

The standard form of a quadratic equation is f(x)=a(x-h)²+k, where (h,k) is the vertex of the parabola (maximum/minimum value)

 

"a" will be the same, but we need to find h and k. You can use a completing the square method to find the vertex, but the easiest way is to use the following formulas.

  

h =-b/(2a)

 

There is no real formula for k, but since (h,k) is a point on our graph, we can plug h into f(x) to get k.

f(h)=k

 

Now, you have f(x)=-2x²+5x-8 this is in general form

a=-2

b=5

c=-8

 

For standard form

a=-2

h=-b/(2a)=-5/(2(-2))=-5/-4=5/4

k=f(h)=-2(5/4)²+5(5/4)-8=-2(25/16)+25/4-8=-50/16+100/16-8=50/16-128/16=-78/16=-39/8

 

So we get, f(x)=-2(x-5/4)²-39/8

 

If you need any clarification, write a message in the comments.