Graph the equation y = -x2 + 5x + 24. How do the values of x = 8 and x = -3 on the graph relate to this situation? Find the width of the archway.

The values of x = 8 and x = -3 are the x-intercepts of this equation. The width of the archway is 11 units.

Step-by-step explanation:

Let be , which is now graphed with the help of a graphing tool, the outcome is included below as attachment. The values of x = 8 and x = -3 are the x-intercepts of this equation, that is, values of x such that y is equal to zero. Algebraically speaking, both are roots of the second-order polynomial.

The width of the archway () is the distance between both intercepts, which is obtained by the following calculation:

, where .

If and , then:

The width of the archway is 11 units.

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