What is the vertex form of #y=5x^2 + 4x - 3?

1 Answer
Nov 16, 2015

#y=5(x+2/5)^2-19/5#

Explanation:

A parabola has the form:
#y=ax^2+bx+c#
#y=5x^2+4x-3#

The vertex form of a parabola is:
#y=a(x-h)^2+k#

To find the vertex #(h,k)# of a parabola we use:

#h =-b/{2a}=-4/{2*5}=-4/10=-2/5=-0.4#

And to find the y coordinate we just evaluate in the original function with the value we just found:

#k=f(-2/5)=5(-2/5)^2+4(-2/5)-3=-3.8#

The vertex is #(-0.4,-3.8)#. Rewriting the equation using the vertex form, we have:

#y=5(x-(-0.4))^2+(-3.8)#
#y=5(x+0.4)^2-3.8#

If you want to have it in a nicer way:

#y=5(x+2/5)^2-19/5#

graph{5(x+2/5)^2-19/5 [-10, 10, -5, 5]}
Click on the graph to see its vertex