Question

Can anybody show me how to do this

Answer 1

To find the x-intercept, substitute in 00 for yy and solve for xx.(0)=−x2+10x−160=-x2+10x-16Since xx is on the right side of the equation, switch the sides so it is on the left side of the equation.−x2+10x−16=0-x2+10x-16=0Factor the left side of the equation.Tap for more steps...−(x−8)(x−2)=0-x-8x-2=0Set x−8x-8 equal to 00 and solve for xx.Tap for more steps...x=8x=8Set x−2x-2 equal to 00 and solve for xx.Tap for more steps...x=2x=2The solution is the result of x−8=0x-8=0 and x−2=0x-2=0.x=8,2x=8,2To find the y-intercept, substitute in 00 for xx and solve for yy.y=−(0)2+10(0)−16y=-02+100-16Solve the equation.Tap for more steps...y=−16y=-16These are the xx and yy intercepts of the equation y=−x2+10x−16y=-x2+10x-16.x-intercept: (8,0),(2,0)8,0,2,0y-intercept: (0,−16)

Answer 2

You want to write this equation in the form (x+...)(x+...) (maybe with a minus sign). To do this, find numbers that, when multiplied, give 16, and when added give -10.

What whole numbers give 16?
1*16 and -1*-16
2*8 and -2*-8
4*4 and -4*-4

Which of these solutions, when changed into a sum, give -10?
Try them one by one and find it is:

-2-8 = -10.

So (x-2)(x-8) is the factorization!

This is really a bit of trial and error, but since most of the time the assignments deals with whole numbers, there aren't that many possibilities.