Question the-qu
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 
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
The quadratic function above models the height above the ground h , in feet, of a
Hard-difficulty · SAT Math · Nonlinear Functions — Quadratic graphs and vertex form. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice D is correct. The positive x-intercept of the graph of is a point 
for which 
. Since 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, 
, 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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