Question

Question #2ab12

Answer 1

`x=-4/3`

Explanation:

There are several ways of finding the minimum value of a parabola.
One is completing the square to get the equation into turning point form. This answer will show an easier way using standard form.

The standard form of a parabola is

`y=ax^2+bx+c`

where `a`, `b` and `c` are constants.

If `a` is positive, then the parabola has a minimum y value, which is given by the turning point.

Luckily, our equation is already in standard form

`y=3x^2+8x+7`

Find `a`, `b` and `c`

`a=3`
`b=8`
`c=7`

`a` is positive so the turning point is going to be the minumum value of `y`.
The easiest way to find the turning point is to use this formula for the x-coordinate

`-b/(2a)`

So plug in the known values

`-b/(2a)=-8/(2*3)=-8/6=-4/3`

Then, substitute this x value into the original equation to find the y value

`y=3(-4/3)^2+8(-4/3)+7=3*16/9-32/3+21/3=5/3`

The coordinates of the turning point, which is the minimum y value of the parabola, are

`(-4/3,5/3)`