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

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.

Step-by-step 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

Step-by-step 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

Step-by-step 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

Step-by-step 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.

botellok botellok · Answer 2 · 2019-08-03T04:36:33+02:00

Answer:

D, C, any, B and B.

Step-by-step explanation:

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

A. [tex]0=x^{2}+3[/tex]

[tex]x^{2}=-3[/tex] this has not solution.

B. In this option occur the same.

C. [tex]0=x^{2}-3[/tex]

[tex]x^{2}=3[/tex]

[tex]x^{2}=\sqrt{3}[/tex] is different to -1.

D. [tex]0=x^{2}-1[/tex]

[tex]x^{2}=1[/tex]

[tex]x^{2}=\sqrt{1}[/tex], 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 [tex](\frac{-b}{2a}, y(\frac{-b}{2a}) )[/tex],

[tex](\frac{4}{8}, 4(1/4)-4(1/2)+4 )[/tex]

[tex](\frac{1}{2}, 3)[/tex] this is not (2,0).

B. [tex](\frac{16}{8}, 4(4)-16(2)+16 )[/tex]

[tex](2, 0)[/tex] 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.