Question

Determine the graph of the quadratic equation y = 3x2 + 10x + 8.

Answer 1

@Limitless Can you help me, pretty pleeeeeeeasee. (:

Answer 2

Well, does it want you to graph it? That's what it means by "determine", right? (It might seem stupid to ask. But different places mean different things by "determine".)

Answer 3

Yes.

Answer 4

All you do is put values in for \(x\) and plot them on graph paper. So, for example: Put \(2\) in for \(x\). You get \(y=3(2)^2+10(2)+8=3(4)+20+8=40.\)

So, one point is \((2,40).\)

It's usually better to start with \(0\) (but you don't have to). \(0\) gives you an easy point \(y=3(0)^2+10(0)+8=0+0+8=8.\) So you have \((0,8)\) as a point.

Just pick some other values and plug them in. You'll have a bunch of points in no time. After that, just graph them. When you connect them, don't draw straight lines. Draw a curved line from point to point.

Answer 5

best to graph the vertex, x intercepts and y intercepts for a quadratic function

Answer 6

@precal, I disagree. \(f(x)=ax^2+bx+c\) is always graphed easily by noticing what inputs result in reasonable outputs. For instance, \((2,40)\) is generally not that great of a point to plot on paper, so you would try to use \(x=1\) instead. And then you'd use the whole axis-of-symmetry and whatnot, thus producing three points...

I get bored at this point. You get my point.

Answer 7

@Limitless It is okay to disagree, however, it is important to take care in plotting the critical points. Later on in mathematics, we referr back to these critical points
In calculus, we will care about the horizontal tangent, (that happens at the vertex),
we will care about where the sign changes, that happens at the roots
Everything we do in the basic classes (example Algebra I) leads us to the thinking required in calculus and beyond.

Answer 8

@precal, I know exactly what you're talking about. I'm telling you the practical nature of things. That is all.
I am a bit offended that you thought I wasn't aware of these things because it's a tad presumptive on your part, but it's all good.