Question

Найдите абсциссы точек пересечения графика функции y=x^2+2.5x-1.5 с осью ох.......

Answer 1

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Answer 2

Finding the Abscissas of the Intersection Points

To find the abscissas of the intersection points of the function \(y = x^2 + 2.5x - 1.5\) with the x-axis, we need to solve for the values of x when y = 0.

The equation of the function is \(y = x^2 + 2.5x - 1.5\). To find the abscissas, we set y to 0 and solve for x:

\(0 = x^2 + 2.5x - 1.5\)

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

\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\]

Where a = 1, b = 2.5, and c = -1.5.

Calculating the Abscissas

Using the quadratic formula, we can calculate the values of x:

\[x = \frac{{-2.5 \pm \sqrt{{2.5^2 - 4*1*(-1.5)}}}}{{2*1}}\]

\[x = \frac{{-2.5 \pm \sqrt{{6.25 + 6}}}}{{2}}\]

\[x = \frac{{-2.5 \pm \sqrt{{12.25}}}}{{2}}\]

\[x = \frac{{-2.5 \pm 3.5}}{{2}}\]

So, the two values of x are:

\[x_1 = \frac{{-2.5 + 3.5}}{{2}} = 0.5\]

\[x_2 = \frac{{-2.5 - 3.5}}{{2}} = -3\]

Conclusion

The abscissas of the intersection points of the function \(y = x^2 + 2.5x - 1.5\) with the x-axis are 0.5 and -3.