How do you find the vertex and the intercepts for # f(x)=-4(x+1)^2+1#?

1 Answer
Dec 9, 2017

The vertex is #(-1,1)# and the intercepts for the #x# axis are #(-1.5, 0)# and #(-0.5,0)# and the intercepts for the #y# axis are #(0, -3)#.

Explanation:

Vertex? If you are using this structure of quadratic equations (#f(x)=a(x-h)^2+k# ) which you are, then the vertex coordinate is #(h,k)#, and in your quadratic equation, that would be #(-1,1)#.

To find the intercepts of #x# and #y# axis, you simply plug in #f(x)=0# into your equation, solve, find two possible answers for #x#, slap a zero, comma, and parentheses next to them and get the coordinates #(-1.5,0)# and #(-0.5,0)#. Then, you plug in #x=0# and do the same for the y axis, in which you will get one answer that is (0, -3).

A really helpful tool to have a visual guide is to use this graphing calculator, desmos.com/calculator where you can plug in any equation you want and have it graph it for you. Good luck on math!