How do you sketch the graph of $y = {(x + 3)}^{2}$ $y=(x+3)^2$ and describe the transformation?

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How do you sketch the graph of $y = {(x + 3)}^{2}$ $y=(x+3)^2$ and describe the transformation?

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Answer 1 · 2017-05-28T12:18:56

$see explanation$ $"see explanation"$

Explanation:

$the graph of y = {(x + 3)}^{2} is the graph of y = x^{2}$ $"the graph of " y=(x+3)^2" is the graph of " y=x^2$
$translated 3 units to the left$ $"translated 3 units to the left"$

$the graph of y = x^{2} is$ $"the graph of " y=x^2" is "$
graph{x^2 [-10, 10, -5, 5]}

$the graph of y = {(x + 3)}^{2}$ $"the graph of " y=(x+3)^2$

$the point (0, 0) \to (- 3, 0)$ $" the point " (0,0)to(-3,0)$

$choosing some values of x$ $"choosing some values of x"$

$x = 0 \to y = 3^{2} = 9 \to (0, 9) \leftarrow y-intercept$ $x=0toy=3^2=9to(0,9)larr" y-intercept"$

$x = - 5 \to y = 2^{2} = 4 \to (- 5, 4)$ $x=-5toy=2^2=4to(-5,4)$

$plot these points and draw a smooth curve through them$ $"plot these points and draw a smooth curve through them"$
$for the graph of y = {(x + 3)}^{2}$ $"for the graph of " y=(x+3)^2$
graph{(x+3)^2 [-10, 10, -5, 5]}

$In general$ $color(blue)"In general"$

$y = f (x + a) is f(x) translated a units left \leftarrow$ $y=f(x+a)" is f(x) translated a units left "larr$

$y = f (x - a) is f(x) translated a units right \to$ $y=f(x-a)" is f(x) translated a units right "rarr$

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How do you sketch the graph of $y = {(x + 3)}^{2}$ $y=(x+3)^2$ and describe the transformation?

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How do you sketch the graph of $y = {(x + 3)}^{2}$ $y=(x+3)^2$ and describe the transformation?