Question

Построить график функции y=3 (x+1)^2 y=3 (x-1)^2

Answer 1

Y=3(x+1)²    корень x=-1    при x=0   y=3
ymin=0  при x=-1   парабола ось симметрии х=-1    убывает при х до -1 и
возрастает при х больших -1
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у=3(х-1)²   корень х=1  при х=0 у=3
умин=0  при х=1   парабола ось симметрии х=1   убывает при х до 1 и возрастает при х больших 1

графики приложены.

Answer 2

Graphing the Functions

To graph the functions y = 3(x + 1)^2 and y = 3(x - 1)^2, we can start by analyzing the equations.

The first equation, y = 3(x + 1)^2, represents a parabola with its vertex at the point (-1, 0). Since the coefficient of the x^2 term is positive, the parabola opens upwards. The value of 3 in front of the parentheses determines the vertical stretch or compression of the parabola.

The second equation, y = 3(x - 1)^2, also represents a parabola with its vertex at the point (1, 0). Similar to the first equation, the parabola opens upwards due to the positive coefficient of the x^2 term. The value of 3 in front of the parentheses determines the vertical stretch or compression of the parabola.

To graph these functions, we can plot a few points and then connect them to form the parabolas. Let's calculate the y-values for a few x-values to get a sense of the shape of the graphs.

For the first equation, y = 3(x + 1)^2: - When x = -2, y = 3(-2 + 1)^2 = 3(1)^2 = 3(1) = 3 - When x = -1, y = 3(-1 + 1)^2 = 3(0)^2 = 3(0) = 0 - When x = 0, y = 3(0 + 1)^2 = 3(1)^2 = 3(1) = 3 - When x = 1, y = 3(1 + 1)^2 = 3(2)^2 = 3(4) = 12 - When x = 2, y = 3(2 + 1)^2 = 3(3)^2 = 3(9) = 27

For the second equation, y = 3(x - 1)^2: - When x = 0, y = 3(0 - 1)^2 = 3(-1)^2 = 3(1) = 3 - When x = 1, y = 3(1 - 1)^2 = 3(0)^2 = 3(0) = 0 - When x = 2, y = 3(2 - 1)^2 = 3(1)^2 = 3(1) = 3 - When x = 3, y = 3(3 - 1)^2 = 3(2)^2 = 3(4) = 12 - When x = 4, y = 3(4 - 1)^2 = 3(3)^2 = 3(9) = 27

Now, let's plot these points on a graph:


The blue curve represents the graph of y = 3(x + 1)^2, and the orange curve represents the graph of y = 3(x - 1)^2. As you can see, both graphs are symmetric with respect to the vertical line x = -1 and x = 1, respectively. The vertex of each parabola is the lowest point on the curve.

I hope this helps! Let me know if you have any further questions.