How do you find the vertex and the intercepts for #y = -4x^2 + 16x - 3#?

1 Answer
Apr 12, 2018

Vertex is #(2,13)#

Explanation:

The vertex of the parabola will be the at he maximum of the

function,i.e, where #dy/dx=0.#

#dy/dx=-8x+16=0#

#=>x=2#
The corresponding value of #y# is #13#

The #y#-intercept will be where #x=0# and the #x#-intercept will be where #y=0 #

So, #y#-intercept #=-3#
x-intercept is the solution of the equation

#" "-4x^2+16x-3=0#

which by solving we get #x=0.197# and #x=3.803# , these are the #x#-intercepts.
graph{-4x^2+16x-3 [-10.82, 21.23, -0.42, 15.6]}
All these can be checked from the graph of the function

.