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Nonlinear functions SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

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

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?

ExplanationShow

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.

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Nonlinear functions SAT question

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