Question

Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y = -0.005x2 + 0.41x - 5.1, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of the rock above the ground. How far horizontally from Landon will the rock land?
A. 66.71 ft
B. 33.35 ft
C. 15.29 ft
D. 7.65 ft

Answer 1

find the derivative ... Equate it with zero

Answer 2

you'll get x

Answer 3

i don't know what you mean

Answer 4

x=15.29007974,66.70992026, y=-5.1 this is what i get

Answer 5

Find the vertex, bro.

Answer 6

how do i find the vertex?

Answer 7

so the answer i got is wrong?

Answer 8

@jollysailorbold , wolfram alpha doesn't help people do the learning part of learning, only the checking answers (unless it's integration lol)

Answer 9

*sexy, do you know how to complete the square?

Answer 10

no

Answer 11

@sexy1993 , is this algebra, or calculus you are learning right now?

Answer 12

algebra

Answer 13

Why don't we do this. Let's start with the basic quadratic equation, and write it in vertex form. Watch please :)

Answer 14

ok

Answer 15

\(ax^2+bx+c=0\) -> divide both sides by a
\(x^2+\frac{b}{a}x+\frac{c}{a}=0\) rewrite again
\(x^2+2(\frac{b}{2a})+\frac{c}{a}=0\)
Everything make sense?

Answer 16

@sexy1993

Answer 17

i'm sorry but i am lost i don't understand

Answer 18

Which line doesn't make sense?

Answer 19

all of it

Answer 20

Ok. We start out with an quadratic equation. Now, a, b, and c, are called constant variables, because we know them when we are given a specific equation, but we are generalizing this. Does that make sense? If not, which part?

Answer 21

yes

Answer 22

Now, x is called the independent variable, and y is called the dependent variable. This is because we don't exactly know values of x and y. But, we can pick values of x, and we have an output "Y", or, y depends on x. Does this make sense?

Answer 23

yes

Answer 24

So, every quadratic equation can be written in the form
\(ax^2+bx+c=y\)

Answer 25

Now, let's rewrite this equation.
@lgbasallote , help; I'm lazy.

Answer 26

why was i called again?

Answer 27

To show @sexy1993 how to write an equation in vertex form so he can solve the problem.