Question

Постройте график функции y=x^2-|4x+3| и определите, при каких значениях m прямая y=m имеет с графиком ровно три общие точки

Answer 1

Строим параболу у=х²-4х-3=(х-2)²-7
Вершина (2;-7)
Оставляем ту часть графика,что справа и строим симметрично ей слева от оси оу.
При m=-3график имеет три общих точки.

Answer 2

Plotting the Function and Finding Common Points with a Line

To plot the function \( y = x^2 - |4x + 3| \) and determine the values of \( m \) for which the line \( y = m \) has exactly three common points with the graph, we can follow these steps:

1. Plotting the Function: - The function is \( y = x^2 - |4x + 3| \). - We can plot the graph of this function to visualize its shape and behavior.

2. Finding Common Points with a Line: - We need to determine the values of \( m \) for which the line \( y = m \) intersects the graph of the function \( y = x^2 - |4x + 3| \) at exactly three points.

Let's start by plotting the function \( y = x^2 - |4x + 3| \) to visualize its graph and then proceed to find the values of \( m \) for which the line \( y = m \) has exactly three common points with the graph.