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# Common Core Standard HSF-IF.C.8a Questions

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

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Use the method of completing the square to find the vertex form of the function $h(d)$. Round computed coefficients and terms to one decimal place, if necessary.
1. $h(d) = -0.0013(d + 246.2)^2 + 0.2$
2. $h(d) = (-0.0013d - 0.6)^2 + 0.2$
3. $h(d) = -0.0013 ( d^2 -246.2) - 60","594.6$
4. $h(d) = -0.0013(d - 246.2)^2 + 78.9$

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What facts about the golf ball's trajectory can be determined directly from the vertex form? Choose all that apply.
1. The amount of time it was in the air for.
2. Its maximum height.
3. At what distance the maximum height occurred.
4. At what time the maximum height occurred.

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Which of the following is the fully factored form of $h(d) ?$ While performing calculations, keep at least 4 decimal places.
1. $h(d) = -0.0013 ( d + 0.2)(d - 492.5)$
2. $h(d) = -0.0013d (d - 492.3) + 0.13$
3. $h(d) = ( d - 0.2)(d + 492.5)$
4. $h(d) = -0.0013 (d + 3.7)(d - 134.4)$

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What information can be determined directly from the factored form of the function $h(d) ?$ Choose all correct answers.
1. The ball's initial height.
2. The total horizontal distance it traveled.
3. The angle the ball was hit at.
4. The total time the ball was in the air for.

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Complete the square so that the function $h(t)$ is in vertex form. Which of the following is correct? Round computed coefficients and terms to one decimal place, if necessary.
1. $h(t) = -4.9(t - 3.1)^2 - 9.4$
2. $h(t) = -4.9(t - 3.1)^2 + 45.9$
3. $h(t) = (-4.9t + 15)^2 - 225$
4. $h(t) = -4.9(t + 3.1)^2 + 9.4$

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What facts about the rocket can be seen directly from the vertex form of the function? Choose all that apply.
1. The time when the rocket reached its maximum height.
2. The total duration of the rocket's flight.
3. The initial velocity of the rocket.
4. The rocket's maximum height.
Grade 9 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8a

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Which of the following is the correct fully factored form of the function $h(t) ?$
1. $h(t) = (2.2t - 5.5)(2.2 + 5.5)$
2. $h(t) = 4.9(t^2 + 6.1t)$
3. $h(t) = -4.9t (t - 6.1)$
4. $h(t) = (-4.9t - 3)(t + 10)$

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What information about the rocket can be directly seen from the factored form of $h(t) ?$ Choose all that apply.
1. The initial height height.
2. The total duration of the flight.
3. The velocity when the rocket reaches its maximum height.
4. How far the rocket traveled.
If you complete the square for $x^2-10x=14$, what will the factored quadratic be?
1. $(x-5)^2=39$
2. $(x-5)^2=114$
3. $(x+5)^2=114$
4. $(x+5)^2=39$
$y = x^2 - 10x + 22.$
1. $y = (x - 11)^2 + 5$
2. $y = (x - 5)^2 - 3$
3. $y = (x +5)^2 +3$
4. $y = (x - 5)^2 + 3$