Create an equation. use the graph below to create the equation of the rainbow parabola.
graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0.
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.

Remember that a quadratic with two real zeroes can be written as , where is a constant and and are the zeroes (or roots) of the function. Since the graph shows that the two zeroes are at -6 and 6, the equation has to be of the form

, or


To solve for a, let's use the point at the vertex (0, 36) and plug that in:




(It makes sense that is negative since the parabola opens down.)

So, the equation of the parabola is

, or


Now for the second part, just pick any two points with which we can draw a line with a positive slope. I'll use x = -2 and 1:




So, our two points are (-2, 32) and (1, 35). To find the equation of the linear function that goes through these two points, let's use slope-intercept form, which is . The slope is given by , so


So, the equation of the linear function so far is just , and we can find by plugging in one of the points on the line:




Thus, the equation of the linear function is



And you can find more points on the line simply by plugging other values of x, such as (0, 34) and (5, 39).

1.   an exact solution requires a radical solution - no decimal approximation.2. (a)4x^3 = 756x^3 = 756/4 = 189x =   cube root of 189 =   5.74   to nearest hundredth answer(b)   189 = 3*3*3*7   so we can write the cube root of 189 as 3∛7 answerchecking (a) 4*(5.74^3 =   756.48   which is very close(b)   4* ((3∛3)^3   = 4*189   = 756   - spot on! 3. i would use solution b because the original question asked for an exact solution.