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

Question

Savannah Anderson · Accepted Answer

Vertex = (4,2)

You can use the vertex formula or put the quadratic in vertex form to determine the vertex of a quadratic equation: First method: Vertex formula The coefficients for the first, second, and third terms in the quadratic are denoted by the letters a, b, and c, respectively. #Vertex = (-b/(2a) , f(x))# Since a = 1 and b = -8 in this instance, entering these values into the previous formula yields: #Vertex = (-(-8)/(2*1) , f(-(-8)/(2*1)))# which turns into: #Vertex = (4 , 4^2 -8*4+18 )# which reduces to: #Vertex = (4 , 2 )# Step 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# b = -8 and c = 18 in this instance. When we change these variables, we obtain #(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.