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Advanced Math / Nonlinear functions Difficulty: Hard

$h of x equals, negative 16 x squared, plus 100 x, plus 10$

The quadratic function above models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If $y equals h of x$ is graphed in the xy-plane, which of the following represents the real-life meaning of the positive x-intercept of the graph?

The initial height of the projectile

The maximum height of the projectile

The time at which the projectile reaches its maximum height

The time at which the projectile hits the ground

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Explanation

Choice D is correct. The positive x-intercept of the graph of $y equals, h of x$ is a point $with coordinates x comma y$ for which $y equals 0$ . Since $y equals, h of x$ models the height above the ground, in feet, of the projectile, a y-value of 0 must correspond to the height of the projectile when it is 0 feet above ground or, in other words, when the projectile is on the ground. Since x represents the time since the projectile was launched, it follows that the positive x-intercept, $the point with coordinates x comma 0$ , represents the time at which the projectile hits the ground.

Choice A is incorrect and may result from misidentifying the y-intercept as a positive x-intercept. Choice B is incorrect and may result from misidentifying the y-value of the vertex of the graph of the function as an x-intercept. Choice C is incorrect and may result from misidentifying the x-value of the vertex of the graph of the function as an x-intercept.