Question

Find the vertex of y=(2x-7)(2x-1) and graph

Answer 1

Explanation:

`y=(2x-7)(2x-1)\\1.\ x=0\\y=(2*0-7)(2*0-1)\\y=(0-7)(0-1)\\y=(-7)(-1)\\y=7\\Thus,\ (0,7)\\2.\ y=0\\0=(2x-7)(2x-1)\\2x-7=0\\2x-7+7=0+7\\2x=7`

Divide both parts of the equation by 2:

`x=3.5\\Thus,\ (3.5,0)\\\\2x-1=0\\2z-1+1=0+1\\2x=1`

Divide both parts of the equation by 2:

`x=0.5\\Thus,\ (0.5,0)`

`3.\ Finding\ the\ vertex\ of\ a \ parabola \\y=(2x-7)(2x-1)\\`

Open parentheses:

`y=2x*2x+2x*(-1)-7*2x-7*(-1)\\y=4x^2-2x-14x+7\\y=4x^2-16x+7\\a=4 \ \ \ \ b=-16\ \ \ \ c=7\\\displaystyle\\x_v=(-b)/(2a) \\\\x_v=(-(-16))/(2*4) \\\\x_v=(16)/(8) \\\\x_v=(2*8)/(8)\\\\x_v=2\\\\Hence, \\\\y_v=(2*2-7)(2*2-1)\\y_v=(4-7)(4-1)\\y_v=(-3)(3)\\y_v=-9\\Thus, (2,-9)`

Plotting a graph by points: