kidzay
27.06.2019 •
Mathematics
What is the vertex form of the quadratic y = 3x^2 + 18x - 4?
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Ответ:
y = 3(x + 3)² - 31
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
take out a common factor of 3 from the first 2 terms
y = 3(x² + 6x) - 4
add/subtract ( half the coefficient of the x-term)² to x² + 6x
y = 3(x² + 2(3)x + 9 - 9 ) - 4
y = 3(x + 3)² - 27 - 4
y = 3(x + 3)² - 31 ← in vertex form
Ответ:
Domain : [-4,4} or
Zeros of the function: (-2, 0, 2)
Intervals when function is positive: (0,2)
Intervals where function is negative: (-4,0), (2,4)
Step-by-step explanation:
Domain can be defined as the input of all possible values of x in the given interval. We can se from the graph that minimum value of x is -4 while maximum value of x is 4. So
The value of function becomes 0 at three places, when x becomes -2,0 or 2
We can see that the function is negative throughout the interval (-4,0), then it become positive from (0,2), then it becomes negative again from (2,4)