Math help. Which is a true statement about the graph of the equation y=x(squared)-7x-60?

Question

1. It is tangent to the x-axis
2.It does not intersect the x-axis
3.It intersects the x-axis in two distinct points that have
4. It intersects the x-axis in two distinct points that have rational coordinates

Answer 1

if you plot this function, you will see it has two points of intersection with the x axis, if you solve the quadratic equation, you will find that there are two real roots of this equation

the solution to this quadratic is

x=[7 +/- sqrt[49+240]]/2
=[7+/-17]/2
x=12, -5 and these are the points where the graph will intersect the x axis

Answer 2

it intersects the x-axis at y = 0
so x^2 - 7x - 60 = 0
(x + 5)(x - 12) = 0
x = 12 or x = -5

so the answer is it intersects the x-axis at two distinct points that have rational coordinates (4)

Answer 3

4. It intersects the x-axis in two distinct points that have rational coordinates

why ??

y=x²-7x-60

Put y =0
0=x²-7x-60
(x-12)(x+5)=0
x=12 , x= -5

So the graph intersects x - axis at 12 and -5 .

Answer 4

#4.
this is becaus ethe equation u gav is called a quadratic equation. in this, every value of y has 2 values for x. and since the value of y is suppposed to be 0, then the equation becomes:
x^2-7x-60=0
then we can use the equation solving methods:
x=(-b+/-(sqrt of (b^2-4ac))/2a
in ur equation, a=1,b=-7,c=-60
x=(7+/-(sqrt(49+240))/2
x=(7+/-17)/2
x=(7+17)/2=24/2=12
x=(7-17)/2=-10/2=-5
thus, the graph will intersect the x-axis at two points, 12, and -5.

Answer 5

4. It intersects the x-axis in two distinct points that have rational coordinates

Answer 6

the 1st assertion is genuine. that's because of the fact while it says y=8 it skill that for each factor on the graph, the y-values are all 8. this means that it quite is going to be a rapidly horizontal line, this is parallel to the x-axis.