Question

How do you write `y=1.4x^2+5.6x+3` in vertex form?

Answer 1

`y=1.4(x+2)^2-2.6`

Explanation:

`y=1.4x^2+5.6x+3` is in the form `y=ax^2+bx+c`

To find the `x` coordinate of the vertex, use the formula `x=-b/(2a)`

`x=-b/(2a) = -5.6/(2*1.4) = -2`

To find the y coordinate of the vertex, plug `x=-2` into the equation.

`y = 1.4(-2)^2 +5.6(-2)+3= -2.6`

The vertex is `(-2,-2.6)`

Use the formula for the vertex form of a quadratic.
`y=a(x-h)^2+k` where `(h,k)` is the vertex.
`y=a(x+2)^2-2.6`

To find the constant `a`, find a convenient point that satisfies the original equation. Typically, the y intercept is found, because the algebra is simple. In other words, find `y` when `x=0`.

`y=1.4(0)^2+5.6(0)+3=3`
Thus, a point that satisfies the equation is `(0,3)`

Use this point to find `a` by substituting it into the equation for the vertex.
`3=a(0+2)^2-2.6`
`3=4a-2.6`
`5.6=4a`
`a=1.4`

Substituting `1.4` for `a` into the vertex form equation gives
`y=1.4(x+2)^2-2.6`

There is another process for converting standard form to vertex form called completing the square. If you need to learn this method, please comment, and I will add it to the answer.