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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Let's start by making a table of values for both functions.

$x$ | $-21 x_{2}$ | $f(x)=-21 x_{2}$ | $-21 x_{2}+1$ | $g(x)=-21 x_{2}+1$ |
---|---|---|---|---|

$-4$ | $-21 (-4)_{2}$ | $-8$ | $-21 (-4)_{2}+1$ | $-7$ |

$-2$ | $-21 (-2)_{2}$ | $-2$ | $-21 (-2)_{2}+1$ | $-1$ |

$0$ | $-21 (0)_{2}$ | $0$ | $-21 (0)_{2}+1$ | $1$ |

$2$ | $-21 (2)_{2}$ | $-2$ | $-21 (2)_{2}+1$ | $-1$ |

$4$ | $-21 (4)_{2}$ | $-8$ | $-21 (4)_{2}+1$ | $-7$ |

Now, to compare the graphs, we will draw them on the same coordinate plane. To do so, we will plot and connect the obtained points for each function.

We see that both parabolas have common characteristics.

- Both graphs open downward, and therefore their vertices are maximum points.
- They have the same shape.
- The parabolas have the same axis of symmetry, which is the vertical line $x=0$ — or $y-$axis —.

Conversely, they also have different characteristics.

- The graph of $g(x)=-21 x_{2}+1$ is a translation of the graph of $f(x)=-21 x_{2}$ up $1$ unit.
- The graph of $g(x)=-21 x_{2}+1$ has two $x-$intercepts, and the graph of $f(x)=-21 x_{2}$ intercepts the $x-$axis only once, which coincides with the vertex.