Question

Нарисовать график квадратичной функцииf(x) = −x2 + 4x−4

Answer 1

Для начало найдем точки пересечения с осиью ОХ , для этого приравняем к 0 
$-x^2+4x-4=0\\ -(x-2)^2=0\\ x=2$
х=2 
поставим 0 заместо х для того чтобы найти точки пересечения с осью ОУ
у=-4
Так как перед  x^2 стоит  - то ветви  вниз направлены

Answer 2

Graph of Quadratic Function f(x) = -x^2 + 4x - 4

To draw the graph of the quadratic function f(x) = -x^2 + 4x - 4, we can start by identifying the key points such as the vertex, x-intercepts, and y-intercept.

1. Vertex of the Parabola: - The vertex of the parabola can be found using the formula x = -b/2a. - In this case, the coefficient of x^2 (a) is -1, and the coefficient of x (b) is 4. - Substituting these values into the formula gives us x = -4 / (2*(-1)) = 2. - To find the corresponding y-coordinate, we can substitute x = 2 into the function: f(2) = -2^2 + 4*2 - 4 = -4.

2. X-Intercepts: - To find the x-intercepts, we set f(x) = 0 and solve for x. - The quadratic formula can be used to find the x-intercepts: x = (-b ± √(b^2 - 4ac)) / (2a). - In this case, a = -1, b = 4, and c = -4. - Substituting these values into the quadratic formula gives us the x-intercepts.

3. Y-Intercept: - The y-intercept occurs when x = 0. - Substituting x = 0 into the function gives us the y-intercept: f(0) = -0^2 + 4*0 - 4 = -4.

Plotting the Graph

Now that we have the key points, we can plot the graph of the quadratic function f(x) = -x^2 + 4x - 4 using the identified vertex, x-intercepts, and y-intercept.

Vertex: (2, -4)
X-Intercepts: (0, -4) and (4, -4)
Y-Intercept: (0, -4)

By plotting these points and considering the shape of the parabola, we can draw the graph of the quadratic function f(x) = -x^2 + 4x - 4.