What is the Vertex, Y-intercept, X intercept, and the axis of symmetry of the equation?

y=-4x62+22x+12

Nerd123 Mar 14, 2019

#1**+3 **

I think you might have

y = -4x^2 + 22x + 12

In the form Ax^2 + Bx + C.....the x coordinate of vertex is given by -B / [2A]

So...here the x coordinate of the vertex is -22/ {2 * - 4) = -22/-8 = 11/4 = 2.75

And to find the y coordinate we have -4(11/4)^2 + 22(11/4) + 12 = 42.25

So....the vertex is (2.75, 42.25 )

y intercept.....let x = 0 and we have -4(0)^2 + 22(0) + 12 = 12

x intercept ......let y = 0 and solve for x

0 = - 4x^2 + 22x + 12 divide through by - 2

0 = 2x^2 - 11x - 6 factor

(2x + 1 ) ( x -6) = 0 set each factor to 0 and solve for x and we have x = -1/2 and x = 6

And those are the x intercepts

The axis of symmetry is just x = the x cooordinate of the vertex = 2.75

CPhill Mar 14, 2019