Question

@Michele_Laino

Answer 1

hint:
we can write this:
\[\Large \begin{gathered}
\left( {3{x^2} + 5x - 6} \right) - \left( { - 2{x^2} + 3x + 7} \right) = \hfill \\
\hfill \\
= 3{x^2} + 5x - 6 + 2{x^2} - 3x - 7 = ...? \hfill \\
\end{gathered} \]

Answer 2

next please combine similar terms

Answer 3

(3x^2+2x^2)+(5x+3x)-(7+6)

Answer 4

yes! now you have to continue, for example:
3x^2+2x^2=5x^2

Answer 5

more precisely:
\[\Large \begin{gathered}
\left( {3{x^2} + 5x - 6} \right) - \left( { - 2{x^2} + 3x + 7} \right) = \hfill \\
\hfill \\
= 3{x^2} + 5x - 6 + 2{x^2} - 3x - 7 = \hfill \\
\hfill \\
= \left( {3{x^2} + 2{x^2}} \right) + \left( {5x - 3x} \right) + \left( { - 6 - 7} \right) = ...? \hfill \\
\end{gathered} \]

Answer 6

so, \(5x-3x=...?\)
and \(-6-7=...?\)

Answer 7

2x
-13

Answer 8

correct!
So, we get:
\[\Large \begin{gathered}
\left( {3{x^2} + 5x - 6} \right) - \left( { - 2{x^2} + 3x + 7} \right) = \hfill \\
\hfill \\
= 3{x^2} + 5x - 6 + 2{x^2} - 3x - 7 = \hfill \\
\hfill \\
= \left( {3{x^2} + 2{x^2}} \right) + \left( {5x - 3x} \right) + \left( { - 6 - 7} \right) = \hfill \\
\hfill \\
= 5{x^2} + 2x - 13 \hfill \\
\end{gathered} \]

Answer 9

@Michele_Laino

Answer 10

the requested average rate, is givenquent formula:
\[r = \frac{{f\left( { - 1} \right) - f\left( { - 3} \right)}}{{ - 1 - \left( { - 3} \right)}}\]

Answer 11

f(1)?

Answer 12

we can write this:

\[\begin{gathered}
f\left( { - 1} \right) = 2{\left( { - 1} \right)^2} - 3\left( { - 1} \right) - 4 = ...? \hfill \\
\hfill \\
f\left( { - 3} \right) = 2{\left( { - 3} \right)^2} - 3\left( { - 3} \right) - 4 = ...? \hfill \\
\end{gathered} \]

Answer 13

23

Answer 14

we can write this:
\[\begin{gathered}
f\left( { - 3} \right) = 2{\left( { - 3} \right)^2} - 3\left( { - 3} \right) - 4 = \hfill \\
\hfill \\
= 2 \cdot 9 + 9 - 4 = 23 \hfill \\
\end{gathered} \]
whereas:
\[\begin{gathered}
f\left( { - 1} \right) = 2{\left( { - 1} \right)^2} - 3\left( { - 1} \right) - 4 = \hfill \\
\hfill \\
= 2 \cdot 1 + 3 - 4 = 2 + 3 - 4 = ...? \hfill \\
\end{gathered} \]

Answer 15

1

Answer 16

correct!
So, we have:
\[r = \frac{{f\left( { - 1} \right) - f\left( { - 3} \right)}}{{ - 1 - \left( { - 3} \right)}} = \frac{{1 - 23}}{{ - 1 + 3}} = ...?\]

Answer 17

-11

Answer 18

that's right!