Question

What is the y-coordinate of the vertex of a parabola with the following equation `y = x^2 - 8x + 18`?

Answer 1

Vertex = (4,2)

Explanation:

To find the vertex of a quadratic equation you can either use use the vertex formula or put the quadratic in vertex form:

Method 1: Vertex formula

a is the coefficient of the first term in the quadratic, b is the coefficient of the second term and c is the coefficient of the third term in the quadratic.

`Vertex = (-b/(2a) , f(x))`

In this case a = 1 and b = -8, so substituting these values into the formula above gives:

`Vertex = (-(-8)/(2*1) , f(-(-8)/(2*1)))`

which becomes:

`Vertex = (4 , 4^2 -8*4+18 )`

which simplifies to:

`Vertex = (4 , 2 )`

Method 2: Vertex form

vertex form looks like this: `(x-h)^2+k`

To convert from quadratic form to vertex form substitute the variables in the next equation with the coefficients of the quadratic `(x+b/2)^2 +c-(b/2)^2`

In this case b = -8 and c = 18

Substituting these variables we get

`(x-8/2)^2 +18-(-8/2)^2`

Which becomes:

`(x-4)^2 +18-4^2`

which simplifies to:

`(x-4)^2 +2`

This is called the vertex form because the vertex can be easily found in this form.

`Vertex = (h,k)`

`Vertex = (4,2)`

Note: This method can be quicker than the first method but only works when the coefficient of a is 1.