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graph the function y=(x-3)² + 4 by transforming the base function y=x​

Sagot :

Abasolodavemarkidn

Answer:

by transforming the base function y=x​

Step-by-step explanation:

Solution.

1. Since g(x) = (x + 2)2 − 3 = f(x + 2) − 3, Theorem 1.7 instructs us to first subtract 2 from

each of the x-values of the points on y = f(x). This shifts the graph of y = f(x) to the left

2 units and moves (−2, 4) to (−4, 4), (−1, 1) to (−3, 1), (0, 0) to (−2, 0), (1, 1) to (−1, 1) and

(2, 4) to (0, 4). Next, we subtract 3 from each of the y-values of these new points. This moves

the graph down 3 units and moves (−4, 4) to (−4, 1), (−3, 1) to (−3, −2), (−2, 0) to (−2, 3),

(−1, 1) to (−1, −2) and (0, 4) to (0, 1). We connect the dots in parabolic fashion to get

__________________________________________________________

From the graph, we see that the vertex has moved from (0, 0) on the graph of y = f(x)

to (−2, −3) on the graph of y = g(x). This sets [−3, ∞) as the range of g. We see that

the graph of y = g(x) crosses the x-axis twice, so we expect two x-intercepts. To find

these, we set y = g(x) = 0 and solve. Doing so yields the equation (x + 2)2 − 3 = 0, or

(x + 2)2 = 3. Extracting square roots gives x + 2 = ±

√

3, or x = −2 ±

√

3. Our x-intercepts

are (−2 −

√

3, 0) ≈ (−3.73, 0) and (−2 + √

3, 0) ≈ (−0.27, 0). The y-intercept of the graph,

(0, 1) was one of the points we originally plotted, so we are done.

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