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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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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 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Convert the quadratic function f(x)=2x2−8x+6 into vertex form.
  1. 2(x−2)2−2
  2. 2(x−4)2+1
  3. (x−2)2+3
  4. 2(x+2)2−3
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor f(x)=4x2-16x+15, and find the zeros.
  1. Zeros:32,52
  2. Zeros:2,54
  3. Zeros:52,3
  4. Zeros:34,5
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor the quadratic function f(x)=x2−7x+10, and find the zeros.
  1. Zeros: x=−2,5
  2. Zeros: x= 2,5
  3. Zeros: x=−5,-2
  4. Zeros: x=5, -1
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
What are the x-intercepts of the quadratic function f(x)=x2−6x+9?
  1. x=1
  2. x=3
  3. x=9
  4. x=6
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 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor f(x)=x2+13x+42 then find the zeros.
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Given f(x)=3x2−12x+9, factor the quadratic function and find the zeros.
  1. Zeros: 1,-3
  2. Zeros: 1,3
  3. Zeros: 2, 1
  4. Zeros: 3,2
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Convert the quadratic function f(x)=2x2+8x+6 into vertex form by completing the square, and find the vertex.
  1. Vertex: (−2,−2)
  2. Vertex: (−2,4)
  3. Vertex: (2,3)
  4. Vertex: (−4,1)
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
What are the zeros of the quadratic function f(x)=x2−4x−5?
  1. x=1,−5
  2. x=1, 5
  3. x=-1,−5
  4. x=5,−1
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor f(x)=x2+10x+25 and find the zeros.
  1. x=0,5
  2. x= 5
  3. x=-5,0
  4. x= -5
Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

This question is a part of a group with common instructions. View group »

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(t2+6.1t)
  3. h(t)=-4.9t(t-6.1)
  4. h(t)=(-4.9t-3)(t+10)
Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor f(x)=-x2-4x+32 then find the zeros.
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Determine the zeros of the quadratic function f(x)=x2−16.
  1. Zeros:x=±4
  2. Zeros:x=±8
  3. Zeros:x=0,4
  4. Zeros:x=-4,16
Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a
Factor the quadratic function f(x)=3x2−9x+6, and find the zeros.
  1. Zeros: x=1,3
  2. Zeros: x=−1,3
  3. Zeros: x=1,2
  4. Zeros: x=0,2
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