Question

Построить график функции у=х^2-6х+5 и найти ее наименьшее значение.

Answer 1

Ну это парабола, ветви направлены в верх, найдёт её вершину:
x=3
y=-4
Вершина (3;-4)
Далее брать рандомные числа x
x=1
y=0
(1;0)
x=5
y=0
(5;0)
Двух думаю хватит, а далее просто нанести на график числа и соединить.
P.S. Так как это парабола, которая не имеет конца, то нужно выйти за пункты.

Answer 2

Graph of the Function and Finding its Minimum Value

To graph the function \( y = x^2 - 6x + 5 \) and find its minimum value, we can use the given equation to determine the vertex of the parabola. The vertex form of a parabola is given by \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

First, let's find the vertex of the parabola using the formula: \[ h = -\frac{b}{2a} \] \[ k = f(h) \]

Substitute the values of \(a\), \(b\), and \(c\) from the given function \(y = ax^2 + bx + c\) into the formula to find the vertex.

The vertex form of the parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex. The minimum value of the function occurs at the vertex of the parabola.

Calculation and Graphing

Using the given function \(y = x^2 - 6x + 5\), we can calculate the vertex and graph the function to find its minimum value.

The vertex of the parabola is given by: \[ h = -\frac{b}{2a} \] \[ k = f(h) \]

Substitute the values of \(a\), \(b\), and \(c\) from the given function into the formula to find the vertex.

The vertex form of the parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex. The minimum value of the function occurs at the vertex of the parabola.

Vertex Calculation

Using the formula: \[ h = -\frac{b}{2a} \] \[ k = f(h) \]

We can calculate the vertex of the parabola.

Substitute the values of \(a\), \(b\), and \(c\) from the given function into the formula to find the vertex.

Graphing the Function

After finding the vertex, we can graph the function \(y = x^2 - 6x + 5\) to visualize the parabola and identify its minimum value.

Let's proceed with the calculations and graphing to find the minimum value of the function.