Question

How do I do this?

Answer 1

Draw a picture

Answer 2

Place the parabola so that it's vertex lies on the y axis. The dog will start at the point (2,0) since the start of the ramp is 2 ft from the peak of the ramp

The vertex is at the point (0,6) because the peak is 6 ft at this point

By symmetry, there's another point on this parabola and it is (-2,0)

Use the three points:
(2,0)
(0,6)
(-2,0)
to determine the equation of the parabola

Answer 3

tried that

Answer 4

how do i make that into an equation though

Answer 5

y = ax^2 + bx + c
6 = a(0)^2 + b(0) + c ... plug in (x,y) = (0,6)
c = 6


y = ax^2 + bx + c
0 = a(2)^2 + b(2) + c ... plug in (x,y) = (2,0)
0 = 4a+2b+c
4a+2b+c = 0
4a+2b+6 = 0 ... plug in c = 6
This is the first equation


y = ax^2 + bx + c
0 = a(-2)^2 + b(-2) + c ... plug in (x,y) = (-2,0)
0 = 4a-2b+c
4a-2b+c = 0
4a-2b+6 = 0 ... plug in c = 6
This is the second equation

Answer 6

So you now have this system
4a+2b+6 = 0
4a-2b+6 = 0
add up the two equations to eliminate b. Then solve for 'a'

Answer 7

Tell me what you get when you solve for 'a'

Answer 8

2/3?

Answer 9

incorrect

Answer 10

adding up the two equations gives

8a+0b+12 = 0
8a+12 = 0
a = ???

Answer 11

-2/3?

Answer 12

you're dividing in the wrong order

Answer 13

8a + 12 = 0
8a = -12
a = -12/8
a = -3/2
a = -1.5

Answer 14

agreed?

Answer 15

ohhh i divided wrong
got it
thx

Answer 16

so we know a = -1.5 and c = 6. What is the value of b?