Question

A polynomial function can be written as (x - 2)(x - 3)(x + 5). What are the x-intercepts of the graph of this function?

(2, 0), (3, 0), (-5, 0)

(-2, 0), (-3, 0), (5, 0)

(2, 0), (3, 0), (5, 0)

(-2, 0), (-3, 0), (-5, 0)

Answer 1

here,
f(x)= (x-2)(x-3)(x+5)

X intercepts are those points at which the value of the function is 0 or the y coordinate is 0.

Here, in the question it is asked to find the values of x for which f(x) =0

so, it will be (x-2)(x-3)(x-5)=0

so, just equate each term on the LHS to 0

so x-2=0
x-3=0 and x+5=0

by solving you shall find the values of X for which the y coordinate is zero.



ref: http://coolmath.com/algebra/08-lines/images/03-lines-01.gif

Answer 2

thank you :)

Answer 3

wait so witch option choice? @praxer

Answer 4

x-2=0 => x=2
x-3=0 => x=3
x+5=0 =>x=-5

so the points shall be
(2, 0), (3, 0), (-5, 0)

Answer 5

thank youuu

Answer 6

$$\huge\color{gold}{Welcome}$$

Answer 7

can you help with another?

Answer 8

Surely I shall try my best :)

Answer 9

The scatter plot shows the number of pages scanned (y) in different number of hours (x) by a scanning machine:

Plot ordered pairs 0, 500 and 1, 1500 and 2, 2500 and 3, 3500 and 4, 4500 and 5, 5500

Which function best represents the data shown in the scatter plot?

y = 100 + 1,000x

y = 100 - 1,000x

y = 500 - 1,000x

y = 500 + 1,000x

Answer 10

@praxer

Answer 11

all the equation above are in the slope intercept form.

the general equation of the slope intercept form is y=mx+c, where m is the slope and c is the y intercept or the value of the function when x=0.

now the formula for the slope is (y'-y")/(x'-x")
where y',y",x',x" are plots on the graph.

now from the above data, if we want to find the slope than lets take values and find the slope from the above slope formula.

here slope shall be = 1500-500/1-0 remember you can take any pair of y and x coordinate. hence the slope is found to be 1000. so, m is found out which =1000

for the y intercept or the c value we have to find the plot when x is = 0.

since we are given with a ordered pair (0,500). Hence from the definition of the y intercept we have c=500

so the equation shall be

y=mx+c

we have m=1000 and c=500

so, the equation is y=1000x+500

Answer 12

oh wow thank you