Question

Построить график функции Y=X²-4x+7

Answer 1

Y=x²-4x+7=(x-2)²+3
Парабола у=х²,ветви вверх,вершина в точке (2;3),х=2-ось симметрии,точки пересечения с осями (0;7)

Answer 2

Graph of the Function y = x² - 4x + 7

To graph the function y = x² - 4x + 7, we can plot several points and connect them to form a curve. Let's start by finding a few points on the graph.

To find the x-intercepts, we set y = 0 and solve for x:

0 = x² - 4x + 7

Using the quadratic formula, we can find the x-values:

x = (-(-4) ± √((-4)² - 4(1)(7))) / (2(1))

Simplifying the equation, we get:

x = (4 ± √(16 - 28)) / 2

x = (4 ± √(-12)) / 2

Since the discriminant is negative, there are no real solutions for x. This means the graph does not intersect the x-axis.

To find the y-intercept, we set x = 0:

y = (0)² - 4(0) + 7

y = 7

So the y-intercept is (0, 7).

We can also find the vertex of the parabola using the formula x = -b / (2a), where a and b are the coefficients of x² and x, respectively:

x = -(-4) / (2(1))

x = 2

To find the corresponding y-value, we substitute x = 2 into the equation:

y = (2)² - 4(2) + 7

y = 4 - 8 + 7

y = 3

So the vertex of the parabola is (2, 3).

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

| x | y | |---|---| | 0 | 7 | | 2 | 3 |

We can also find additional points by substituting different values of x into the equation. For example, when x = 1:

y = (1)² - 4(1) + 7

y = 1 - 4 + 7

y = 4

So another point on the graph is (1, 4).

By plotting these points and connecting them, we can obtain the graph of the function y = x² - 4x + 7.


Please note that the graph is a parabola that opens upwards, and it does not intersect the x-axis. The vertex of the parabola is located at (2, 3), and the y-intercept is at (0, 7).

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