Answer:
A: y = (x − 4)^2 − 4
Step-by-step explanation:
vertex=(4.-4)
A: y = (x − 4)^2 − 4
y=x^2-8x+16-4
y=x^2-8x+12 (a=1,b=-8,c=12)
the y intercept is (0,12)
vertex ( h, k)
h=-b/2a ⇒ h=-(-8)/2=4
plug the value of h in the equation y=x^2-8x+12
k=4²-8(4)+12
k=16-32+12
k=-4
v(4,-4)
Answer:
greater than 7
Step-by-step explanation:
Answer:
Take a look at the 'proof' below
Step-by-step explanation:
The graph of the function g(x) is similar to that of the function f(t). The local minimum, local maximum, absolute minimum, maximum etc... of 'x' is always the closest x-intercept of the graph of f(t).
Let's check if this statement is right. The two local minimum(s) of the function f(t) occurs at x = 2, and x = 6. The two local maximum(s) occur at 1/4 and 4. As you can see the maximum / minimum of the function g(x) is always an x-intercept, x = 3, x = 7.
For part (b) the absolute maximum value of the function f(t), is 8. The closest x-intercept is 9, which is our solution.
Answer:
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Using the stated transformation, the graph of g(2x) is given at the end of the answer.
<h3>Horizontal stretch and compression</h3>
An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:
g(x) = f(ax).
The definition of stretch or compression depends on the value of the constant a, as follows:
- If a > 1, it is a compression by a factor of 1/a.
- If a < 1, it is a stretch by a factor of 1/a.
In this problem, the rule is:
f(x) = g(2x).
Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:
That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.
More can be learned about transformations at brainly.com/question/28725644
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