Finding roots and interval increase and decrease of quadratic functions. Help me :)

Question

Gdeinward · Answer

Oh what fun. Please expand on what you need help with

jhonyy9 · Answer

do you know what is a quadratic function ?

Allison · Answer

Yes

Allison · Answer

@dude

Allison · Answer

$$y=x ^{2}+4$$

Allison · Answer

Vertex (0,4)
AOS x=0
Opens up (minimum)

Hero · Answer

Set y = 0 then solve for x

Allison · Answer

x is 0

Hero · Answer

That's only for the vertex

Hero · Answer

To find the roots, you have to set y = 0 then solve for x

Hero · Answer

Actually, I realize that the roots are imaginary in this case.

Allison · Answer

So it's (x,0)..?

justjm · Answer

Imaginary means no x-intercepts. |dw:1575752642669:dw|

Allison · Answer

How do I find x? Can I do it on my calculator?

justjm · Answer

The root would be a complex number, plug it into the quadratic formula and simplify

Hero · Answer

The roots are imaginary means that x is not a real number when y = 0.

Allison · Answer

What??

Hero · Answer

To find the interval of increase, you have to observe the graph. The vertex is where the graph is neither increasing nor decreasing. That's the lower limit of the interval of interest.

Allison · Answer

(4,0)?

Allison · Answer

OH WAIT

Hero · Answer

To find roots:
Set  $y = 0$ then solve for $x$:

$0=x^2+4$. Can you solve for $x$ from here?

Hero · Answer

One thing at a time

Hero · Answer

One thing at a time. Try solving for $x$ first. You're trying to do two things at once.

Allison · Answer

x is 0

Hero · Answer

Only the $x$ coordinate of the vertex is zero. x is not zero for the entire graph.

Allison · Answer

Ahh I have no idea what you're saying :(

Hero · Answer

|dw:1575753114080:dw| $x$ is 0 for that point only which is the vertex, the lowest point,  of the graph.

Allison · Answer

Yes

Hero · Answer

However, to find the roots of the graph, you have to set y = 0, then solve for $x$ as I was trying to get you to do here: $\color{#0cbb34}{\text{Originally Posted by}}$ @Hero
To find roots:
Set  $y = 0$ then solve for $x$:

$0=x^2+4$. Can you solve for $x$ from here?
$\color{#0cbb34}{\text{End of Quote}}$

Allison · Answer

..no

Allison · Answer

104?

Hero · Answer

Where are these numbers you're spewing coming from? From where did you get 104?

Allison · Answer

Wait if y is 0, so is x??

Allison · Answer

I put x^2+4 in the calculator and got 104

Hero · Answer

Okay, let's do an example

Hero · Answer

Suppose $y = x^2 + a$ where $a$ is any positive real number.

Allison · Answer

Aka 4

Hero · Answer

To find the roots of the function, the rule is to set $y = 0$ then solve for $x$ as follows:

$0 = x^2 + a$

Next subtract $a$ from both sides:

$-a = x^2$

Next isolate $x$ by applying the root to both sides:
$\sqrt{-a} = \sqrt{x^2}$

Simplify:
$\sqrt{a}\sqrt{-1} = x$

$\sqrt{a}i = x$ 
$i$ is an imaginary number.

Hero · Answer

That's what you're supposed to do to find the roots of $x$ and actually it should add a $\pm$ symbol

Allison · Answer

Equals 0 because y is also 0 now and x is 0

..RIGHT?

Allison · Answer

I haven't learned that symbol

Hero · Answer

I already explained how to find the roots.

Allison · Answer

o.0

Hero · Answer

And I explained where $x = 0$ which has nothing to do with finding the roots.

Allison · Answer

._. what

Allison · Answer

Then how do I get the roots? The points where the line touches the axis on the graph?

Allison · Answer

I was JUST starting to like math thinking I understand it

Hero · Answer

As you can observe from the graph, there are no points on $y = x^2 + 4$ touching the $x-$ axis.

Allison · Answer

Yeah, it's only touching the y-axis

Hero · Answer

Exactly, so that tells you that there are no real roots of the graph.

Hero · Answer

Which mean the same thing as there are no points where the function touch the x-axis.

Allison · Answer

Oh my sadjghgasdkh THIS WHOLE TIME AND THERE ISN'T ONE

Hero · Answer

When I said the roots of the function are imaginary, that implies no real roots.

Allison · Answer

Well how was I supposed to get that from that?

Hero · Answer

Most users get that when we say the roots of the function are imaginary. You're the first user in QC/OS history that didn't get it.

Hero · Answer

At least the first user that didn't get it when I said it.

Allison · Answer

LOL

Hero · Answer

Which from that, I can determine how much you've been studying.

Allison · Answer

I just try to understand it

Gdeinward · Answer

Sometimes, hero, you have to write in lamens terms and explanations to explain something. Never have I had any problems teaching someone something, even Allison

Hero · Answer

There's different levels of lamens terms

Hero · Answer

layman's*

Gdeinward · Answer

but I must admit, it was quite hard to teach Allison that, cant say I wouldnt of had as much trouble

Allison · Answer

I feel dumb now :(