Question

How do you find the x and y intercepts for `f(x)=2(x-5)^2 -50`?

Answer 1

Intercepts on `x`-axis are `0` and `10`; intercept on `y`-axis is `0`.

Explanation:

In the function `f(x)=2(x-5)^2-50`, `x`-intercept is given by `f(x)=0` and `y`-intercept is given by `f(0)`.

As such `x`-intercept is given by `2(x-5)^2-50=0` i.e. `2(x^2-10x+25)-50=0` or

`2x^2-20x=0` or `2x(x-10)=0` i.e. `x=0` and `x=10`.

`y`-intercept is `f(0)=2(0-5)^2-50=2*25-50=0`.

Hence while intercepts on `x`-axis are `0` and `10`; intercept on `y`-axis is `0`.