Question

How do you find the max or minimum of `f(x)=7x^2+4x+1`?

Answer 1

This is a quadratic equation, which is a parabola, and the coefficient of the `x^2` term is positive .

Explanation:

This means the parabola will open upwards , and the vertex is a minimum.

First let's find the x-coordinate of the vertex: `-b/(2a)` is the formula for that:
`-4/(2*7) = -4/14 = -2/7`. This vertical line, `x=-2/7` is also the axis of the parabola.

The y-coordinate of the vertex is: `(4ac-b^2)/(4a)`, which gives us:

`(4*7*1 - 4^2)/(4*7)`, which = `(28 - 16)/28 = 12/28 = 3/7`.

So the vertex, v = `(-2/7, 3/7)` and it's a minimum.

(It's after one in the morning as I do this, so re-check my arithmetic above.)

Connie