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1 answer:
According to the <em>dilation</em> formula, the location of the four vertices of the quadrilateral A'B'C'D' are A'(x, y) = (0, 0), B'(x, y) = (0, 7.5), C'(x, y) = (12.5, 7.5) and D'(x, y) = (12.5, 0).
<h3>How to determine the coordinates of the vertices of the dilated rectangle</h3>
Dilation are a kind of <em>rigid</em> transformations defined by the following formula:
P'(x, y) = O(x, y) + r · [P(x, y) - O(x, y)] (1)
Where:
- O(x, y) - Center of dilation
- r - Dilation factor
- P(x, y) - Original point
- P'(x, y) - Resulting point
If we know that r = 2.5, O(x, y) = (0, 0), A(x, y) = (0, 0), B(x, y) = (0, 3), C(x, y) = (5, 3) and D(x, y) = (5, 0), then the resulting points are obtained:
A'(x, y) = (0, 0) + 2.5 · [(0, 0) - (0, 0)]
A'(x, y) = (0, 0)
B'(x, y) = (0, 0) + 2.5 · [(0, 3) - (0, 0)]
B'(x, y) = (0, 7.5)
C'(x, y) = (0, 0) + 2.5 · [(5, 3) - (0, 0)]
C'(x, y) = (12.5, 7.5)
D'(x, y) = (0, 0) + 2.5 · [(5, 0) - (0, 0)]
D'(x, y) = (12.5, 0)
Lastly, we proceed to graph the two figures.
To learn more on dilations: brainly.com/question/13176891
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Answer:
The inverse of f(x) is (x) = ±
+
Step-by-step explanation:
To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where
- h =
- k is the vlue f at x = h
∵ f(x) = 3x² - 3x - 2
→ Compare it with the 1st form above to find a and b
∴ a = 3 and b = -3
→ Use the rule of h to find it
∵ h = =
=
∴ h =
→ Substitute x by the value of h in f to find k
∵ k = 3( )² - 3(
) - 2
∴ k =
→ Substitute the values of a, h, and k in the vertex form above
∵ f(x) = 3(x - )² +
∴ f(x) = 3(x - )² -
Now let us find the inverse of f(x)
∵ f(x) = y
∴ y = 3(x - )² -
→ Switch x and y
∵ x = 3(y - )² -
→ Add to both sides
∴ x + = 3(y -
)²
→ Divide both sides by 3
∵ = (y -
)²
→ Take √ for both sides
∴ ± = y -
→ Add to both sides
∴ ± +
= y
→ Replace y by (x)
∴ (x) = ±
+
∴ The inverse of f(x) is (x) = ±
+