Question

Hi you guys! I need some help finding the discriminate of "y=x^2-13x+42.25".. Would anyone like to help? :)

Answer 1

1. Scary pic.
2. Did you mean the "discriminant"?

Answer 2

discriminant is b^2-4ac

a 1
b -13
c 42.25

Answer 3

Is that all that is to it? Yes, I do mean discriminant lol sorry!!
And thank you thank you, my pic is very scary I suppose :p

Answer 4

So when solving, do I leave out "a" and solve with just b and c by plugging them into the above equation?

Answer 5

Yes, that is all to it. @rulnick has very nicely given you the values of a, b and c. Using these values, you find what the expression \(b^2 - 4ac\) evaluates to.

Answer 6

In a quadratic \(ax^2 + b x+ c = 0\), \(b^2 - 4ac\) is the discriminant.

Answer 7

I got -169-169, I don't feel as if this is correct :c Am I right?

Answer 8

Well, almost so. But \(b^2 = (-13)^2 = 169\) as the square of a negative is also positive.

Answer 9

ah, because a negative and negative multiplied together creates a positive. So the CORRECT answer would be 169-169? Thank you for helping btw :D

Answer 10

Yes... what is 169 minus 169?

Answer 11

zero

Answer 12

So the discriminant is zero?

Answer 13

yes

Answer 14

So, would you mind steering me in the next direction? I need to know which would be the best method of finding the x-intercepts algebraically.. I'm not quite sure how to go about knowing this

Answer 15

The x-intercept is when the value of the quadratic becomes zero.

Answer 16

My homework would like to know though, would factoring, quadratic formula, completing the square, etc. be the best method of solving

Answer 17

So based off of what I have, How am I sure?

Answer 18

For this case, you can use any of the above.

Answer 19

Oh alright, well that's awesome for my assignment! :) Would any of them be a better choice to go with?

Answer 20

Really, I'd prefer none over the other. But one thing that's worth a mention: did you know that a quadratic with discriminant zero is a perfect square?

Answer 21

No, I didn't happen to know this, but I did just get done working with perfect squares awhile ago in my AlgII course and I'm familiar with them. And thank you, I'll just pick one and solve; I appreciate your time! c:

Answer 22

No problem! I may prove it to you using the quadratic formula, if you want...

Answer 23

I would love to watch! Just more demonstration for me, which is helpful always

Answer 24

\[x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\]Note how that thing within the square root is the discriminant? That's the reason why it's so important to calculate. Anyway, if the discriminant is zero, then\[x = \dfrac{-b \pm \sqrt{0}}{2a}=\dfrac{-b}{2a}\]So basically, we get only one unique root.

But you know that a quadratic with only one unique root is a perfect square...

Answer 25

Oh my, it makes perfect sense now that I see how it is related and comes together

Answer 26

Haha!