Question

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

Answer 1

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!