A system of equations is shown

Mathematics

2 answers:

Degger [83]3 years ago

6 0

$\bf \begin{cases}
\boxed{y}=3x-2\\
y=x^2
\end{cases}~\hspace{6em}\stackrel{\textit{doing a quick substitution}}{\boxed{3x-2}=x^2}\implies 0=x^2-3x+2
\\\\\\
0=(x-1)(x-2)\implies
\begin{cases}
0=x-1\implies &1=x\\[0.8em]
0=x-2\implies &2=x
\end{cases}
\\\\[-0.35em]
~\dotfill$

$\bf \stackrel{\textit{using x = 1 in the first equation}}{y=3(1)-2\implies y=1}~\hfill \blacktriangleright (\stackrel{x}{1},\stackrel{y}{1}) \blacktriangleleft
\\\\\\
\stackrel{\textit{using x = 2 in the first equation}}{y=3(2)-2\implies y=4}~\hfill \blacktriangleright (\stackrel{x}{2},\stackrel{y}{4})\blacktriangleleft$

Wewaii [24]3 years ago

3 0

no the first one is (2,4) and then (1,1)

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yaroslaw [1]

I believe so yes this is correct I think

4 0

3 years ago

Omg please help please

Brut [27]

$x^{2}$ Answer:

(Explanation)

Step-by-step explanation:

Part A:

The graph of y = $x^{2}$ + 2 will be translated 2 units up from the graph of y = $x^{2}$ .

If you plug in 0 for x, you get a y-value of 2. The 2 is also not included with the $x^{2}$ , which is why it doesn't translate left.

This is what graph A should look like:

[Attached File]

Part B:

The graph of y = $x^{2}$ - 2 will be translated 2 units down from the graph of y = $x^{2}$ .

If you plug in 0 for x, you get a y-value of -2. The 2 is also not included with the $x^{2}$ , which is why it doesn't translate right.

This is what graph B should look like:

[Attached File]

Part C:

The graph of y = 2 $x^{2}$ is a stretched version of the graph y = $x^{2}$ . Numbers that are greater than 1 stretch and open up and numbers less than -1 stretch and open down.

This is what graph C should look like:

[Attached File]

Part D:

The graph of y = $\frac{1}{2}x^{2}$ is a compressed version of the graph y = $x^{2}$ . Numbers that are in-between 0 and 1, and -1 and 0 are compressed.