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

1 Answer
May 13, 2018

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.