How many times does the graph of this function intersect or touch the x-axis: y = -3x^2 + x + 4?

Question

Thanks in advance for the help.

Answer 1

It's a parabola - it crosses the X axis only once. I graphed it on the calculator and it crosses once.

Answer 2

How do you go about answering this question? If you don't know, where were you when it was covered in class? Or where is your textbook? You have got to know this stuff, or you'll get nowhere. See your teacher and do your homework. This is a quadratic equation. It intersects in either 0, 1, or two locations. Make a plot by plugging in numbers for x and calculating y. Plot the numbers. For x= -2, -1, 0, 1, 2, y = -10, 0, 4, 2, -6 and so on.
You will see that there are two intersections with the x-axis. These are called roots of the polynomial. This is no hard, but you have to start paying attention, and getting into it...

Answer 3

y = -3x^2 + x + 4

Determining how many times this intersects the x-axis is as simple as determining how many solutions this has, after setting y = 0. After all, when y = 0, we determine our x-intercepts.

0 = -3x^2 + x + 4

Use the quadratic formula.

x = [-1 +/- sqrt(1 - 4(-3)(4)] / 2(-3)
x = [-1 +/- sqrt(1 + 48)] / (-6)
x = [-1 +/- sqrt(49)] / (-6)
x = [-1 +/- 7]/(-6)

So our two solutions are
x = { [-1 + 7]/(-6) , [-1 - 7]/(-6) }
simplified,

x = {-1, 4/3}

We have two solutions, which implies the curve touches the x-axis twice.

Answer 4

it does not touche the x-axis at all. The graph is a parabola that starts at y=4 upwards.

Answer 5

This consists to search the roots

x1 = (-1+(1+48)^0.5)-6 = (-1+7)/-6= -1
AND

x1 = (-1-(1+48)^0.5)-6 = (-1+7)/-6= 4/3

The parabola cuts x axis at points -1 and +4/3

It works

Answer 6

two times

the arms are down
a<0

delta>0
V(1/3,4)

x-intercept points
(-1,0) and (4/3,0)