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

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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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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Grade 9 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8a
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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Using the information given, which of the following functions has the correct values for the constants $T_a, T_0, k ?$
1. $T(t) = 210 + 135 e^(-0.34 t)$
2. $T(t) = 75 + 135 e^(-0.075 t)$
3. $T(t) = 75 + 210 e^(-0.19 t)$
4. $T(t) = 75 + 35 e^(0.26 t)$
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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Using laws of exponents, re-write the function $T(t)$ into the form $T(t) = a*b^t + c$, where $a,b,c in RR$.
1. $T(t) = 1.445 * (1.078)^t + 75$
2. $T(t) = 0.692 * (0.928)^t + 75$
3. $T(t) = 135 * (1.078)^t + 75$
4. $T(t) = 135 * (0.928)^t + 75$
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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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. $h(t) = -4.9(t + 3.1)^2 + 9.4$
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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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 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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Why are the numbers for the percent rate of change calculated in the previous two questions not the same?
1. Because the calculations didn't use exact numbers, and therefore there are rounding errors.
2. Because the function has an added constant (it is not of the form $ab^x$).
3. Because the percent rate of change calculated from the different form of the function, $T(t) = a*b^t + c$, is a general rate of change, which is not the same as the specific rate of change from $t=1$ to $t=2$.
4. Because an exponential function is not constant, therefore its percent rate of change shouldn't be constant.
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. $h(t) = (-4.9t - 3)(t + 10)$