Question

How do you determine the vertex of the parabola `y=3x^2-24x+53`?

Answer 1

The vertex is `(4,5)`.

See the explanation.

Explanation:

Determine the vertex:

The vertex of a parabola represented by a quadratic equation represents the maximum or minimum point of the equation. The vertex is determined by solving for the `x` and `y` of the ordered pair that forms the vertex. The generic form of a quadratic equation is `ax^2+bx+c`, where `a and b` are the coefficients, and `c` is the constant.

`y=3x^2-24x+53`

Determine `a,b,andc`.

`a=3`, `b=-24`, `c=53`

Determine the value for `x`.

`x=-b/(2a)`

`x=-(-24)/(2*3)`

`x=24/6`

`x=4`

Now plug `4` back into the equation, substituting for `x`, and solve for `y`.

`y=3x^2-24x+53`

`y=3(4)^2-24(4)+53`

`y=3*16-96+53`

`y=48-96+53`

`y=5`

The vertex is point `(4,5)`.

graph{3x^2-24x+53 [-16.43, 15.6, -1.78, 14.25]}