Question

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.

Create an equation. Use the graph below to create the equation of the rainbow parabola.

Answer 1

y = a(x - p)(x - q)

p and q are the zeros of the parabola, -6 and 6
y = a(x + 6)(x - 6)

Substitute third point (0, 36) into the above equation to solve for a.

Answer 2

@peachpi so i plug 0 in for x and then 36 i plug it in where the y is?

Answer 3

yes

Answer 4

is the answer a=-1? @peachpi

Answer 5

yes

Answer 6

can you help me on the next question please?? @peachpi

Answer 7

if i can

Answer 8

Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.

Answer 9

3)Analyze the two functions. Answer the following reflection questions in complete sentences.

What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?
What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.
Is the linear function you created positive or negative? Explain.
What are the solutions or solution to the system of equations created? Explain what it or they represent.

Answer 10

Pick two points that the parabola goes through and then write the equation of the line that connects them.

Answer 11

What points would be the easiest?

Answer 12

any two points where gridlines meet. Or if you have a graphing calculator you can pick points with integers or simple fractions

Answer 13

5,5?

Answer 14

i mean 5,10

Answer 15

The line has to intersect the parabola twice AND move upward.
You need a lower point on the left side and a higher point on the right side

Answer 16

You chose 5 on the right, but that won't really work with moving upward. Try -5 on the left, and plug it into the equation we found above to find the y-coordinate.

Answer 17

i am so confused like idk where to even start.

Answer 18

when you plug -5 into the equation we got for the first part, what do you get?

Answer 19

what do i plug it in for? which variable

Answer 20

for x. to solve for y

Answer 21

so y=-1(-5+6)(-5-6)? then solve?

Answer 22

yes

Answer 23

y=11?

Answer 24

yes. Now pick an x-value on the right side and do the same thing to get the other point.