Answer:
c. Shift the graph of y = x^2 right 2 units and then down 15 units
Step-by-step explanation:
Replacing x in f(x) with (x-a) shifts the graph to the right by "a" units. Adding "b" to f(x) to make it f(x)+b shifts the graph up by "b" units.
Here, we have "a" = 2 and "b" = -15 to turn f(x) = x^2 into f(x-2)-15 = (x-2)^2-15. So, the graph is shifted ...
Parabola is a curve. To transform the graph of y = x² to y = (x - 2)² - 15, Shift the graph of y = x² right 2 units, and then down 15 units.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to us
y = x²
y = (x - 2)² - 15
We know that the function y = x² is the function of a parabola if we compare it to the general equation of a parabola,
y = a(x-h)² + k
y = x²
We will find the value of the constant a is 1, while the coordinates of the vertex of the parabola are (0,0), therefore, the origin.
Now, comparing the general equation of a parabola with the second function given to us,
y = a(x-h)² + k
y = (x - 2)² - 15
We can see that the value of the constant a is 1, while the coordinate of the vertex of the parabola is (2, -15).
If we compare the two of the given function we will find that the value of the constant of both functions is the same which is 1, therefore, both the parabolas are of the same width and will open upside, the only difference between them is that the coordinates of the two are different.
Thud, in order to transform the graph of y = x² to y = (x - 2)² - 15, we need to shift the coordinates of the vertex of the parabola 2 units right(2), and 15 units down(-15).
Hence, to transform the graph of y = x² to y = (x - 2)² - 15, Shift the graph of y = x² right 2 units, and then down 15 units.
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