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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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Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

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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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Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Convert the quadratic function f(x)=x2-10x+25 into vertex form and identify the vertex.
  1. Vertex:(-5,0)
  2. Vertex:(-5,25)
  3. Vertex:(5,25)
  4. Vertex:(5,0)
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
What are the zeros of the function f(x)=x2+2x15?
  1. Zeros:x=3,5
  2. Zeros:x=5,3
  3. Zeros:x=1,-15
  4. Zeros:x=1,15
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
If $5,000 is invested at 8% interest compounded semi-annually, what function models the investment after t years?
  1. A(t)=5000(1+0.08)2t
  2. A(t)=5000(1+0.082)2t
  3. A(t)=5000(1+0.04)2t
  4. A(t)=5000(1+0.08)t
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
If h(x)=()(1.5)x, what type of change does the function represent?
  1. Exponential growth
  2. Exponential decay
  3. Constant
  4. Linear growth
Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

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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 abx).
  3. Because the percent rate of change calculated from the different form of the function, T(t)=abt+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.
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Complete the square for f(x)=x2+4x+1, then find the vertex.
  1. Vertex:(-2,-3)
  2. Vertex:(2,1)
  3. Vertex:(-2,-1)
  4. Vertex:(-2,-5)
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor f(x)=x25x+6, and find the zeros.
  1. Zeros: 2,3
  2. Zeros: -2,3
  3. Zeros: 1,6
  4. Zeros: 2,-3
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