Question

Need help with Quadratic formula:
0 = 16x^2+vx+s
and
x=-b±√b^2 - 4ac /2a

Motor A Vertex coordinates(Just the name of one of our problems): (5.9375, 564.0625)

My teacher said to use the 0 = 16x^2+vx+s formula first and use one of the coordinates in place of v, and then we are supposed to go to the second formula and find both solutions to x.
She said that one of the x's will equal 0, so I am trying to find the other x in the integer form but I'm not sure which coordinate I need to substitute into v.
Can someone help me out?

Answer 1

@haileemackk
first of all this is not a quadratic equation , i believe that there has been a typing mistake it should have been
0 = 16x^2+vx+s

now since there are 3 unknowns at present x, v and s
you said we have to put the value of v, even then irrespective of which ever coordinate you put you will be left with s as the unknown so this means that you will not be able to solve the quadratic equation...

please check you question again and try to clarify a bit more

Answer 2

The first formula is the projectile formula and I believe the second is the quadratic equation. And I did mean 0 = 16x^2+vx+s, sorry for the confusion.

This is what my teacher gave us:
Imagine you are a fountain designer and you need to know how different speed motors will affect the water’s projected height and time in the air. You have various motor speed options but need to choose the one that most closely meets the client’s height request of 690 feet. Your job is to determine which motor speed is the best choice. In all cases, you will use the projectile formula
y = –16x2 + vx + s, with starting height of 0 (s = 0).

The equation for motor A is: y = -16x^2 + 190x + 0 so that means
a = -16 b = 190 c = 0

Motor A Vertex coordinates: (5.9375, 564.0625)

I know need to find the x intercepts so I can graph them, but like you said - with the coordinates I have, you can't solve it. I'm not sure what I've done wrong.

Answer 3

well
y = -16x^2 + 190x + 0 this is solvable
do you know how we calculate the ymax (maximum height) of the projectile?

Answer 4

Well, we had to graph y = -16x^2 + 190x + 0 and then find the points on the parabola.
On the graph it said:
a = (0,0)
b = (11.875 , 0)
c = (5.9375, 564.0625)

Answer 5

See http://www.khanacademy.org/math/algebra/quadratics/quadratic_formula/v/using-the-quadratic-formula
for how to do this

meanwhile, for your specific problem
y = -16x^2 + 190x + 0
you don't need the quadratic formula to find the 2 x-intercepts
but we can use it.

first, match your equation to
y = a x^2 + b x + c
y = -16x^2 + 190x + 0

a = -16, b= 190, c=0

use those numbers in
\[ x = \frac{1}{2a} (-b ± \sqrt{b^2 -4ac} )\]
in other words, replace the letters with their corresponding numbers
\[ x = \frac{1}{2\cdot -16} \left(-190 ± \sqrt{(-190)^2 -4(-16)\cdot 0} \right )\]

Answer 6

that simplifies to
\[ x= -\frac{1}{32}\left( -190 ±190\right) \]
or
\[ x= -\frac{1}{32}\left( -190 +190\right) = 0\]
and
\[ x= -\frac{1}{32}\left( -190 -190\right) =\frac{380}{32}= \frac{95}{8}= 11.875\]
just as you say in your post.

Answer 7

The vertex is the highest point on the parabola (it looks like an arc)
to plot it, you plot (0,0), the highest point (5.9375, 564.0625), and (11.875,0)
then connect the dots

Answer 8

But I don't understand your specific question. Can you ask it again ?

Answer 9

you say **so I am trying to find the other x in the integer form**

the other x (where the parabola hits the ground) is not an integer. x is \( 11 \frac{7}{8} \)

Answer 10

the question asks
*** Your job is to determine which motor speed is the best choice. In all cases, you will use the projectile formula
y = –16x2 + vx + s, with starting height of 0 (s = 0).***


I am guessing you are given a few motors with different speeds "v"
***choose the one that most closely meets the client’s height request of 690 feet.**

I think that means find the motor that comes closest to y=690 for its vertex.
the x value of the vertex is at -b/2a
where a and b come from
y= a x^2 + bx + c

Do you have to find the vertex in this problem or do they tell it to you ?

Answer 11

Thanks for such a detailed answer! It really helped me finish my homework. I suppose you were right about it not being an actual integer so I might have misheard her. Also, we had to find three different motors but she solved motor A with us and said that was the one we would be using.