Question

Graph: -4p^2+80p please. I'm not sure how to get the x intercepts.

Answer 1

hi

Answer 2

Well, the x intercepts occur when y = 0 right? so we can just set your equation = to 0 and find out what P will be

\[\large -4p^2 + 80p = 0\]

Answer 3

-4p(p -20) = 0

Answer 4

There are a few ways to do this...we can use the quadratic formula, we can complete the square...or we can just graph and see where the parabola passes through the x-axis

Answer 5

How do you complete the square?

Answer 6

So to complete the square...takes a little more work than normal.....

\[\large -4p^2 + 80p = 0\]

Start by dividing everything by the -4...we want that p^2 alone...so

\[\large p^2 - 20p = 0\] we start with this

Answer 7

We now take the coefficient of the p term...so -20 here

we divide it by 2....so -20 / 2 = -10

Then we square this result

(-10)^2 = 100

So this 100...is what we add to each side of our equation

\[\large p^2 - 20p + 100 = 100\]

Answer 8

Now...we write the left side as a square...what 2 numbers multiply to make 100 but also add to make -20? well...-10 and -10 do

So we write it as

\[\large (p - 10)^2 = 100\]

Answer 9

Is this the easiest way to solve?

Answer 10

....it's easy when you do it a bunch of times...practice makes it speedier...but the easiest way to solve it would be to see what @triciaal posted..

if you factor out a -4p from the equation you had

you get

\[\large -4p(p - 20) = 0\]

what 2 values of p make this equation = 0?

Answer 11

0!?