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Did you notice the double rainbow in the picture?

a double rainbow over a mountain range with an arrow emphasizing the second rainbow
The double rainbow image is superimposed on the grid with two parabolas, each emphasizing the shapes of the rainbows. The first rainbow has the parabolic function h of x is equal to negative one eighth times x squared plus three halves x minus eleven eighths. The second rainbow has the parabolic function q of x equals negative one eleventh times x squared plus twelve elevenths x plus thirteen elevenths.

Note: The function q of x equals negative one eleventh times x squared plus twelve elevenths x plus thirteen elevenths can be used to model the upper rainbow in the double rainbow.

Answer the following questions about the quadratic equation.



Tip

Vertex form of a quadratic function is written in the form y equals a times the quantity x minus h squared plus k. The vertex of the parabola is (h,k).

Factored form of a quadratic function is written in the form y equals a times the quantity x minus m times the quantity x minus n. The zeros of the function are m and n.