Respuesta :
"no x-intercept(s)" => graph never even touches the x-axis.
y = mx^2 – 5x – 2 is the equation of a parabola that opens up.
The quadratic formula would be useful here. Note that there are 3 possible outcomes when this formula is applied: the discriminant b^2 - 4ac could be zero, positive or negative. If the discrim. is negative, then the roots (solutions) are complex; the graph does not touch the x-axis.
So, let's find the discrim. of y = mx2 – 5x – 2. here a=m, b= -5 and c= -2. The discrim. is b^2 - 4(a)(c), or (-5)^2 - 4(m)(-2), or 25+8m. For which values of m is 25+8m<0? Subtracting 25 from both sides, we get 8m < -25, or m<25/8.
Let's check this. Let m=3 (which is less than 25/8). Does the curve ever touch the x-axis? y = 3x^2 - 5x - 2; here a=3, b= -5 and c= -2. Then the discriminant is 25-4(3)(-2) = 49 (which is positive), so there would be two different, real roots (x-intercepts). No good.
Looking at y=mx^2 - 5x - 2 once more, we see that if x=0, y = -2, so for any m, the curve goes thru the point (0,-2), so long as m is positive.
Now let's look at the possibilities for negative m. Suppose we have
y = -3x^2 - 5x - 2. Then the discriminant would be 25-4(-3)(-2), or 1. So we'd have 2 real, unequal roots yet again.
As a last resort, I used my calculator repeatedly to graph y=mx^2 - 5x - 2. I found that if m is less than about -3.125, there is/are no x-intercept. (answer)
y = mx^2 – 5x – 2 is the equation of a parabola that opens up.
The quadratic formula would be useful here. Note that there are 3 possible outcomes when this formula is applied: the discriminant b^2 - 4ac could be zero, positive or negative. If the discrim. is negative, then the roots (solutions) are complex; the graph does not touch the x-axis.
So, let's find the discrim. of y = mx2 – 5x – 2. here a=m, b= -5 and c= -2. The discrim. is b^2 - 4(a)(c), or (-5)^2 - 4(m)(-2), or 25+8m. For which values of m is 25+8m<0? Subtracting 25 from both sides, we get 8m < -25, or m<25/8.
Let's check this. Let m=3 (which is less than 25/8). Does the curve ever touch the x-axis? y = 3x^2 - 5x - 2; here a=3, b= -5 and c= -2. Then the discriminant is 25-4(3)(-2) = 49 (which is positive), so there would be two different, real roots (x-intercepts). No good.
Looking at y=mx^2 - 5x - 2 once more, we see that if x=0, y = -2, so for any m, the curve goes thru the point (0,-2), so long as m is positive.
Now let's look at the possibilities for negative m. Suppose we have
y = -3x^2 - 5x - 2. Then the discriminant would be 25-4(-3)(-2), or 1. So we'd have 2 real, unequal roots yet again.
As a last resort, I used my calculator repeatedly to graph y=mx^2 - 5x - 2. I found that if m is less than about -3.125, there is/are no x-intercept. (answer)
The value of m is less than -3.125 does the graph [tex]y = mx^2 - 5x - 2[/tex] has no x-intercept.
We have to determine, the value of m for does the graph [tex]y = mx^2 - 5x - 2[/tex] have no intercept.
According to the question,
[tex]y = mx^2 - 5x -2[/tex] is the equation of a parabola that opens up.
The quadratic formula would be useful here.
There are 3 possible outcomes when this formula is applied: the discriminant [tex]b^2 - 4ac[/tex] could be zero, positive or negative.
If the discriminant is negative, then the roots (solutions) are complex; the graph does not touch the x-axis.
Therefore,
To find the discriminant of graph = [tex]y = mx^2 - 5x -2[/tex].
[tex]D = b^2-4ac[/tex]
Where, a = 1, b =-5, c=-2.
Then,
[tex]D = (-5)^2-4\times 1 \times (-2)\\\\D = 25+8\\\\D = 33[/tex]
Then, The value of m is [tex]25+8m<0[/tex]
Subtracting 25 from both sides,
[tex]8m < -25\\\\m = \dfrac{-25}{8}[/tex]
Let, m=3 (which is less than 25/8).
The curve ever touches the x-axis,[tex]y = 3x^2 - 5x - 2;[/tex]
Where a=3, b= -5 and c= -2.
Then the discriminant is = 25-4(3)(-2) = 49 (which is positive),
So there would be two different, real roots (x-intercepts).
Looking at once more, [tex]y=mx^2 - 5x - 2[/tex] see that if x=0, y = -2,
So for any m, the curve goes thru the point (0,-2), so long as m is positive.
Now let's look at the possibilities for negative m.
Suppose, [tex]y=mx^2 - 5x - 2[/tex].
Then the discriminant would be = 25-4(-3)(-2) = 1.
They have 2 real, unequal roots yet again.
Hence, The graph y= [tex]y=mx^2 - 5x - 2.[/tex] found that if m is less than about -3.125, there is no x-intercept.
To know more about the Slope click the link given below.
https://brainly.com/question/2773823
