Question

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.

Answer 1

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

Explanation:

Let be
`y = -x^(2)+5\cdot x +24`, 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 (
`d`) is the distance between both intercepts, which is obtained by the following calculation:

`d = |x_(1)-x_(2)|`, where
`x_(1) \geq x_(2)`.

If
`x_(1) = 8` and
`x_(2) = -3`, then:

`d = |8-(-3)|`

`d = 8 +3`

`d = 11`

The width of the archway is 11 units.