Question

1. Which function has x-intercepts of -1 and 1 and contains the point (2,3)?

A) y=x^2+3
B) y=x^2+1
C) y=x^2-3
D) y=x^2-1

2. Which function has x intercepts of 3 and 8 and contains the point (-1,-2)?
A) y= -(1/36)(x-3)(x-8)
B) y= -(1/14)(x-3)(x-8)
C) y= -(1/18)(x-3)(x-8)
D) y= -(1/7)(x-3)(x-8)

3. Which function has vertex (-3,-1) and contains the point (-1,-9)?
A) y= -(x-3)^2-1
B) y= -(5/8)(x+3)^2-1
C) y= -(3/8)(x-3)^2-1
D) y= -(1/2)(x+3)^2-1

4. Which function has vertex (2,0) and contains the point (3,4)?
A) y= 4x^2-4x+4
B) y= 4x^2-16x+16
C) y= x^2-4x+4
D) y= 2x^2-8x+8

5. What is the equation of quadratic function with vertex (0,0) and containing the points (1,-1), and (-1,-1)?
A) y= x^2
B) y= -x^2
C) y= x^2+1
D) y= x^2-1

Answer 1

D, C, any, B and B.

Explanation:

1. x-intercept is when y=0, so

A.
`0=x^(2)+3`

`x^(2)=-3` this has not solution.

B. In this option occur the same.

C.
`0=x^(2)-3`

`x^(2)=3`

`x^(2)=√(3)` is different to -1.

D.
`0=x^(2)-1`

`x^(2)=1`

`x^(2)=√(1)`, x=1 and x=-1. This is the correct answer.

2. A. 0 = -(1/36)(x-3)(x-8), the solutions are 3 and 8 and for the point (-1,-2):

-2=-(1/36)(-1-3)(-1-8)

-2=-(1/36)(-4)(-9)

-2=-1 and this is not true.

B. The process of x-intercept is the same as A and for the point (-1,-2):

-2=-(1/14)(-1-3)(-1-8)

-2=-(1/14)(-4)(-9)

-2=-18/7 and this is not true.

C. The process of x-intercept is the same as A and for the point (-1,-2):

-2=-(1/18)(-1-3)(-1-8)

-2=-(1/18)(-4)(-9)

-2=-2, this is the correct answer.

3. A. the vertex is (3,-1).

B. The vertex is (-3,-1) and for the point (-1,-9):

-9= -(5/8)(-1+3)^2-1

-9 = -7/2 and this is not true.

C. the vertex is (3,-1).

D. The vertex is (-3,-1) and for the point (-1,-9):

-9= -(1/2)(-1+3)^2-1

-9 = -3 and this is not true.

4. A. the vertex is
`((-b)/(2a), y((-b)/(2a)) )`,

`((4)/(8), 4(1/4)-4(1/2)+4 )`

`((1)/(2), 3)` this is not (2,0).

B.
`((16)/(8), 4(4)-16(2)+16 )`

`(2, 0)` and for the point (3,4):

4= 4(9)-16(3)+16

4=4. This is the correct answer.

5. The only options that have vertex in (0,0) are A and B. For the points:

A. -1 = 1^2 and this is not true.

B. -1 = -(1^2)=-1 and -1=-(-1)^2=-1. This is the correct answer.

Answer 2

Answers:

Question 1.

Choice D.

Explanation:

Substitute x = 2 in the given equations, the equation that yields y =3 is the equation we are asked to determine. Moreover, since we also given the x-intercepts we can confirm our choice by substituting x =1 or x = -1 into the equation. The value of y will be 0.

Question 2.

Choice C.

Explanation:

Substitute x = -1 in the given equations, the equation that yields y =-2 is the equation we are asked to determine. Moreover, since we also given the x-intercepts we can confirm our choice by substituting x =3 or x =8 into the equation. The value of y will be 0.

Question 3.

Choice D

Explanation:

Substitute x = -3 in the given equations, the equation that yields y =-1 is the equation we are asked to determine. The second point can be used to check that the function chosen is actually the required one.

Question 4.

Choice B

Explanation:

Substitute x = 2 in the given equations, the equation that yields y = 0 is the equation we are asked to determine. The second point (3, 4) can be used to check that the function chosen is actually the required one.

Question 5.

Choice B

Explanation:

Substitute x = 0 in the given equations, the equation that yields y = 0 is the equation we are asked to determine. The other two point (1, -1) and (-1, -1) can be used to check that the function chosen is actually the required one.