Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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Steps to solve:
10.2x + 9.4y when x = 2 and y = 3
= 10.2(2) + 9.4(3)
= 20.4 + 28.2
= 48.6
______
Best Regards,
Wolfyy :)
If you have double functions, solve the one in the parentheses first.
in f(g(2)), solve g(2) first.
So, substitute 2 in the function.
g(x) = x^2 - 6x - 7
g(2) = 2^2 - 6(2) - 7 = -15
If you substitute -15 in f(g(2)), it becomes f(-15).
f(x) = x + 8
f(-15) = -15 + 8
f(-15) = -7
The answer for f(g(2)) is -7.
