How do I graph these Quadratic functions?

Chart21

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May 2, 2021
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3
1. f(x) = -1/19x2

Not sure what to do. If this was f(x) = 5x2 I'd do (0,0) as the vertex and make a table to figure out some other points. But I'm really stuck with this super odd fraction. A video told me to use a number that, when squared, is divisible by the fractions denominator. 19 squared is 361! I can't even graph that on my homework. I've also tried using a table and some fractions, but the rise/run fraction works when you don't have an x value already. I'm just really stuck here.

2. f(x) = 2(x-11)2

I know that the vertex is (11, 0). How do I calculate the y value?

Graphing f(x) = a(x-h)^2 is super hard for me. I've looked everywhere online and no one explains it. When I try solving it by using FOIL to turn it into general form, it's wrong. So obviously there's a way to solve these that isn't using general form.
 
1. f(x) = -1/19x2

Not sure what to do. If this was f(x) = 5x2 I'd do (0,0) as the vertex and make a table to figure out some other points. But I'm really stuck with this super odd fraction. A video told me to use a number that, when squared, is divisible by the fractions denominator. 19 squared is 361! I can't even graph that on my homework. I've also tried using a table and some fractions, but the rise/run fraction works when you don't have an x value already. I'm just really stuck here.

2. f(x) = 2(x-11)2

I know that the vertex is (11, 0). How do I calculate the y value?

Graphing f(x) = a(x-h)^2 is super hard for me. I've looked everywhere online and no one explains it. When I try solving it by using FOIL to turn it into general form, it's wrong. So obviously there's a way to solve these that isn't using general form.
I think you have an "aversion" towards plotting decimals. Get over it !! Just scale the y-axis appropriately and plot. The problem (1) will look as follows:

x​
f(x)​
0​
0​
-1​
0.052632​
1​
0.052632​
-2​
0.210526​
2​
0.210526​
-3​
0.473684​
3​
0.473684​

1619974441528.png

Now show us your work for the second problem! For that problem - I would choose x = 11, 10, 12, 9, 13 (symmetrical about the vertex x = 11)
 
Our teacher said she specifically doesn't want to teach us how to graph with decimals because it's too complicated. I guess I'll go find tutorials on how to do that and try that way. The "get over it" was really unnecessary and rude. I literally don't know how to graph with decimals,it's not me being lazy. Thanks for explaining what you have so far.
 
1. Draw the graph of y=[MATH]-x^2[/MATH] and when you've done it, write [MATH]\frac{ }{19}[/MATH] under every number on your y-axis.
2. Just make a table and e.g. when x=3 do (3-11), square it, then multiply by 2
3. You need to draw two separate graphs for when a>0 e.g. draw something that looks like [MATH]y=x^2[/MATH], and when a<0, something like [MATH]y=-x^2[/MATH].
Work out where [MATH]y=a(x-h)^2[/MATH] will have its vertex and where it will cut on the y-axis and label those 2 points.
 
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