Select an answer from the options below and click Submit.
Question 1
Below is the standard form and graph of a quadratic function.
f(x)=x2−16f of x equals x squared minus sixteen
Which of the following equations represents the function in factored form?
Answer: Correct! Go to question 2.
Answer: Incorrect. The answer is C. The parabola crosses the x–axis at -negative4 and 4. These are the zeros. Thus, f(x)=(x+4)(x−4)f of x equals the quantity of x plus four times the quantity of x minus four. Go to question 2.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 2
Below is the standard form and graph of a quadratic function.
f(x)=x2−16f of x equals x squared minus sixteen
Which of the following equations represents the function in vertex form?
Answer: Correct! Go to question 3.
Answer: Incorrect. The answer is D. The minimum of this parabola is (0, -negative16). This is the vertex of the parabola. Thus, f(x)=(x+0)2−16f of x equals the quantity of x plus zero squared minus sixteen. Go to question 3.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 3
Below is the standard form and graph of a quadratic function.
f(x)=-negativex2+2x−1f of x equals negative x squared plus two x minus one
Which of the following equations represents the function in factored form?
Answer: Correct! Go to question 4.
Answer: Incorrect. The answer is A. This parabola only has one zero, which is 1. Note that the parabola extends downwards, so a=-negative1. Thus,
f(x)=-negative(x−1)(x−1)f of x equals the negative of the quantity of x minus one times the quantity of x minus one
or
f(x)=-negative(x−1)2f of x equals the negative of the quantity of x minus one squared. Go to question 4.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 4
Below is the standard form and graph of a quadratic function.
f(x)=-negativex2+2x−1f of x equals negative x squared plus two x minus one
Which of the following equations represents the function in vertex form?
Answer: Correct! Go to question 5.
Answer: Incorrect. The answer is C. Note that the parabola extends downwards, so
a=-negative1. The vertex is at (1,0).
Thus, f(x)=-negative(x−1)2+0f of x equals the negative of the quantity of x minus one squared plus zero.
Go to question 5.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 5
Below is the standard form and graph of a quadratic function.
f(x)=
12x2−5x+212f of x equals one half of x squared minus five x plus twenty one halves
Which of the following equations represents the function in factored form?
Answer: Correct! Go to question 6.
Answer: Incorrect. The answer is D. The zeros of the function are 3 and 7. Thus,
f(x)=12(x−7)(x−3)f of x equals one half the quantity of x minus seven times the quantity of x minus three.
Go to question 6.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 6
Below is the standard form and graph of a quadratic function.
f(x)=
12x2−5x+212f of x equals one half of x squared minus five x plus twenty one halves
Which of the following equations represents the function in vertex form?
Answer: Correct! Go to question 7.
Answer: Incorrect. The answer is B. The vertex of the parabola is (5,-negative2). Thus,
f(x)=12(x−5)2−2f of x equals one half of the quantity of x minus five squared minus two.
Go to question 7.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 7
Below is the standard form and graph of a quadratic function.
f(x)=
-negative12x2−4x+10f of x equals negative one half x squared minus four x plus ten
Which of the following equations represents the function in factored form?
Answer: Correct! Go to question 8.
Answer: Incorrect. The answer is B. The zeros are -negative10 and 2. Thus,
f(x)=-negative12(x+10)(x−2)f of x equals negative one half times the quantity of x plus ten times the quantity of x minus two.
Go to question 8.
Answer:Incorrect. Review the Learn It section, and then try again.
Question 8
Below is the standard form and graph of a quadratic function.
f(x)=
-negative12x2−4x+10f of x equals negative one half x squared minus four x plus ten
Which of the following equations represents the function in vertex form?
Answer: Correct!
Answer: Incorrect. The answer is A. The vertex is at (-negative4,18). Thus,
f(x)=-negative12(x+4)2+18f of x equals negative one half times the quantity of x plus four squared plus eighteen.
Answer:Incorrect. Review the Learn It section, and then try again.
