Few 8th Grade Math Questions?

Question

I got three questions:

1) What is a factor of x^2 - 11x + 24?
A x+3
B x-3
C x+4
D x-4

2) What quantity should be added to both sides of this equation to complete the square? x^2 - 8x = 5

A 4
B -4
C 16
D -16

3) How many times does the graph of
y = 2x^2 - 2x +3 intersect the x-axis?

A none
B one
C two
D three


I also would like to know how to do it. Thank you in advance! I "thumbs up" all answers.

Answer 1

1. x^2-11x+24 simplifies into (x-3)(x-8)



2. x^2-8x=5, the square would be (x-4)^2, so you need to add 16, since (-4)^2=16.



3. at x=0, y=3, which means the parabola starts above the x axis. Since the x^2 part of the equation is positive, the parabola opens upwards, meaning it never crosses the x axis. So A.none.

Answer 2

1) x^2 -11x + 24 = (x -8)(x - 3)

so one of the factor is (x - 3). Ans B



2) x^2 - 8x = 5

Adding 16 on both sides,

x^2 - 8x + 16 = 5 +16

(x -4)(x - 4) = 21

(x-4)^2 = 21

Thereafter you are able to solve the eqaution if required.

So ans is C



3) At x axis y = 0

0= 2x^2 - 2x +3

Since there is no solution to this, there the graph does not intersect the x axis. So ans A.

Answer 3

1) Factor it:

x² - 11x + 24 = (x - 3)(x - 8)

Of your choices, B is correct.



2) To complete the square, add (-8/2)² to each side. The correct answer is C. This is how you would complete the square:

x² - 8x + (-8/2)² = (-8/2)² + 5

(x - 8/2)² = 16 + 5

x - 4 = ± sqrt21

x = 4 ± 3sqrt3



3) To find the zeros, just factor it. Every real factor will contribute one zero. Complex or imaginary factors will not create a zero in the real domain.

2x² - 2x + 3 = 0

x² - x = -1.5

x² - x + (-1/2)² = (-1/2)² - 1.5

(x - 1/2)² = 0.25 - 1.5

x - 0.5 = ± sqrt(-1.25)

x = 0.5 ± 0.5 i sqrt5

The zeros are complex conjugates. The answer is A; the graph never crosses the X-axis.

Answer 4

#1=b

#2=c

#3=a

Answer 5

Answers:

1) B

2) C

3) A



The methods to solve problem 1 and 3 is the quadratic formula which can be best explain here:

http://www.purplemath.com/modules/quadform.htm

for problem 1 you need to find x with the given a=1, b=-11, c=24

for problem 3 you need to find x with the given a=2, b=-2, c=3 and if you get an imaginary number as one of the root then the graph does not intersect the x-axis.



The method to solve problem 2:

is done by finding c in the quadratic formula because we are given a, b, and x.

Answer 6

b (x-3)(x-8)



1/2 of 8 = 4 4^2 =16 c





discirnnant sqrt 4- 24= -20 A none

Answer 7

1. (x -8) (x-3), so the answer is x-3 from your choices



2. (x^2 - 8x + ?) = 5

(x - 4)

Answer 8

I do 8th grade math enough at home and school; sorry, I don't know : (

Answer 9

do your own homework slackerr !