Calculus

algray09

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May 12, 2020
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I have question 6 attached to this, I’m honestly lost.
I think part a it has b^2-4ac has to positive because it’s greater than zero but I don’t know what to say about the function in relation to the x axis.

Part b b^2-4ac=0 wouldn’t the function be on the x axis only cause it’s = 0.

Part C b^2-4ac<0 it has to be negative so wouldn’t the function be below the x axis.

Otherwise I’m totally lost since there aren’t actual values given. Also I find this question to be worded weird.
 

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Steven G

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b^2-4ac=0: No, the function will not be on the x-axis. The function that is only along the x-axis is the line y=0. y=0 is NOT a quadratic equation.

b^2-4ac<0: You say it has to be negative so wouldn’t the function be below the x axis. That is complete nonsense.

What about when b^2-4ac>0?

This question is not weird. It is a question that every algebra student should know the answer to.

Write down some quadratics, graph them and see what happens when b^2-4ac is 0, less than 0 and greater than 0. This is how you learn.

I will start you off with 3 quadratic equation to look at.
y=x^2+4x+4
y= x^2 + 5x + 6
y= x^2 + 4x +17
 

algray09

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Kind of helpful but I need to explain how each relates to the given functions graph and relate to x axis. Actually I had the right thought on x axis just flipped around because greater than zero the function in the graph’s vertex could be below zero because there would be two real roots. = zero the function would have one real root and the vertex could be on the x axis. Less than zero the function would be above the x axis and have no real roots.
Thx for making it more understanding with the equations but,
Questions like these are hard because it’s asking to explain in words. I was able to figure out how to explain each answer your examples helped a little
 

JeffM

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Sep 14, 2012
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Kind of helpful but I need to explain how each relates to the given functions graph and relate to x axis. Actually I had the right thought on x axis just flipped around because greater than zero the function in the graph’s vertex could be below zero because there would be two real roots. = zero the function would have one real root and the vertex could be on the x axis. Less than zero the function would be above the x axis and have no real roots.
Thx for making it more understanding with the equations but,
Questions like these are hard because it’s asking to explain in words. I was able to figure out how to explain each answer your examples helped a little
Really, truly, you need to keep what you learned in algebra and geometry firmly in mind in calculus. Calculus is just the study of certain classes of functions.

What is the general form of a quadratic function in one variable? What is the general form of a quadratic equation in one variable?

How many real solutions may a quadratic equation have? Have you ever heard of the quadratic formula? If so, what is it used for?

Given a quadratic function in one variable, if you turn it into a quadratic equation in standard form, what does that tell you about the function?
 
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