Question

Consider the function y=2x2−60x+270.(a) Find the x-coordinate of the vertex of the graph.(b) Set the viewing window so that the x-coordinate of the vertex is near the center of the window and the vertex is visible, and then graph the given equation.(c) State the coordinates of the vertex

Answer 1

5Our equation is already given in the form of : y = ax^2 +bx +c.

So in order to find the x- coordinate of the vertex , we will calculate

x= -b/2a.

y = 2x^2 -60x + 270 ;

a = 2

b= -60

c = 270

(a) x = -b/2a

x = -(-60)/ 2(2)

x = 60 / 4

x = 15

(b ) lets find the x intercepts in order to be able to draw the graph :

we do this by placing the equation y = 0 .

Therefore : y = 2x^2 -60x +270 = 0

We will use the following function in order to find the x -intercept :

x1, x2 = (-b +-sqr b^2 -4ac) / 2a

x1,x2 = [(--60) +-sqr (-60)^2 -4(2)(270)] / 2(2)

x 1 = 3(5+sqr10)

x2 = 3(5 - sqr 10)

(c) We already have the x vertex that we found in step a = x = 15

in order to find the y - cordinate of the vertex , simply plug in x = 15 into the equation and solve for y:

y = 2(15)^2 - 60 (15) +270

y = 2(225) - 900 +270 = 450 -900 +270

y = -180