Discriminant: use B^2-4ac, find times Ax^2+Bx+C crosses axis

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wallee

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For the following equation: A x square+Bx + C

use the discrimanat which is Bsquare-4ac, and state whether it passes X axis 0,1 or 2 times. I think I did this correct but My answer is that it passes twice, the answer in the book states once. Please help!
 
Re: Discriminant

wallee said:
For the following equation: A x square+Bx + C

use the discrimanat which is Bsquare-4ac, and state whether it passes X axis 0,1 or 2 times. I think I did this correct but My answer is that it passes twice, the answer in the book states once. Please help!
Click to expand...

I'm sorry...

ax[sup:2jtz6qsr]2[/sup:2jtz6qsr] + bx + c

is NOT an equation.

Did you neglect to post your specific problem for us?

If you have an equation like this:

3x[sup:2jtz6qsr]2[/sup:2jtz6qsr] + 4x - 1 = 0

you can use the discriminant to find the number of x-intercepts.

In my example, a = 3, b = 4, and c = -1

The discriminant is b[sup:2jtz6qsr]2[/sup:2jtz6qsr] - 4ac, or in this case,

4[sup:2jtz6qsr]2[/sup:2jtz6qsr] - 4(3)(-1)

or,

16 + 12

or, 28

Since the discriminant is positive, there are TWO real solutions (so the graph crosses the x-axis two times). Since the discriminant is not a perfect square, those x-intercepts are irrational real numbers.
 
Re: Discriminant

thats what I said, but indeed the problem in the book states A x square + B x + C. Once I used the discriminant, I got -3 which states two non real numbers but i still dont get how it passes through a graph once...
 
Re: Discriminant

once i graphed it it crossed the x axis at (-1,0) and (0,0). the answer is that it only passes the x axis once..
 
Re: Discriminant

Please state your original quadratic EQUATION for us.
 
Ok, here is the exact problem straight from the book:

Consider the function: f(x)=ax square+bx+c
If bsquare-4ac=0, determine whether the graph of f(x) will intersect the x-axis at zero, one, or two points.

The name of this section is Roots of Quadratic functions.
The answer that the book has is one, but I am so confused....I didnt even think this was an equation.
 
wallee said:
Ok, here is the exact problem straight from the book:

Consider the function: f(x)=ax square+bx+c
If bsquare-4ac=0, determine whether the graph of f(x) will intersect the x-axis at zero, one, or two points.

The name of this section is Roots of Quadratic functions.
The answer that the book has is one, but I am so confused....I didnt even think this was an equation.
Click to expand...

Seeing the exact question (finally) I believe the book is trying to get you to think about what the value of the discriminant tells you about the quadratic function f(x).

If b^2 - 4ac is positive (b^2 - 4ac > 0), then the function has two UNEQUAL, real zeros and crosses the x-axis twice.
If b^2 - 4ac = 0, then the function has two EQUAL real zeros, and crosses the x-axis only once (the vertex of the parabola which is the graph of such a function lies on the x-axis)
If b^2 - 4ac is negative (b^2 - 4ac < 0), then the function has two COMPLEX zeroes (no real zeros) and does not cross the x-axis at all.

I hope this helps you...and in the future, please remember that it helps US if you type the question exactly as it appears in your book.
 
Thanks, I understand this part however, the answer is one, and I still dont know how they got this. My answer was -3 hence, I had no real roots meaning it didnt cross the x axis once...
 
wallee said:
Thanks, I understand this part however, the answer is one, and I still dont know how they got this. My answer was -3 hence, I had no real roots meaning it didnt cross the x axis once...
Click to expand...

You were given the information that b[sup:3vj7sppd]2[/sup:3vj7sppd] - 4ac = 0. "b[sup:3vj7sppd]2[/sup:3vj7sppd] - 4ac" is called the discriminant of a quadratic function. When the discriminant has a value of 0, the function has two equal roots, which means the graph of the function intersects the x-axis in just one point. So that's how the book came up with its (CORRECT) answer of 1.

You were not given a specific equation with values for a, b, and c. How could you come up with -3?

Uh oh....something just occurred to me....you DIDN'T combine b[sup:3vj7sppd]2[/sup:3vj7sppd] - 4ac and come up with -3, did you??? If that is what you did, then you need more help than we can give you here, and you probably would be wise to contact a tutor who can work with you one-on-one until you get caught up with the background information you are apparently missing.
 
Ok, I understand now.I guess I was just thrown off with the equation that was given. I got -3 by plugging in 1 for the discriminant=(1) square-4(1)(1). I got one because I thought 1 was the coefficient of the equation that was given. (ax square+bx+c)
 
wallee said:
Ok, I understand now.I guess I was just thrown off with the equation that was given. I got -3 by plugging in 1 for the discriminant=(1) square-4(1)(1). I got one because I thought 1 was the coefficient of the equation that was given. (ax square+bx+c)
Click to expand...

The coefficient of x[sup:23xdqfue]2[/sup:23xdqfue] was 'a' , coefficient of x[sup:23xdqfue]1[/sup:23xdqfue] was 'b' and coefficient of x[sup:23xdqfue]0[/sup:23xdqfue] was 'c'
 
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