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Advanced Math Difficulty: Hard

$h of x equals, 2 times, open parenthesis, x minus 4, close parenthesis, squared, minus 32$

The quadratic function h is defined as shown. In the xy-plane, the graph of $y equals, h of x$ intersects the x-axis at the points $with coordinates 0 comma 0$ and $t comma 0$ , where t is a constant. What is the value of t ?

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Explanation

Choice D is correct. It’s given that the graph of $y equals, h of x$ intersects the x-axis at $the point with coordinates 0 comma 0$ and $the point with coordinates t comma 0$ , where t is a constant. Since this graph intersects the x-axis when $y equals 0$ or when $h of x equals 0$ , it follows that $h of 0 equals 0$ and $h of t equals 0$ . If $h of t equals 0$ , then $0 equals, 2 times, open parenthesis, t minus 4, close parenthesis, squared, minus 32$ . Adding 32 to both sides of this equation yields $32 equals, 2 times, open parenthesis, t minus 4, close parenthesis, squared$ . Dividing both sides of this equation by 2 yields $16 equals, open parenthesis, t minus 4, close parenthesis, squared$ . Taking the square root of both sides of this equation yields $4 equals, t minus 4$ . Adding 4 to both sides of this equation yields $8 equals t$ . Therefore, the value of t is 8.

Choices A, B, and C are incorrect and may result from calculation errors.