Question

Постройте график функции y=x^2+2x-6

Answer 1

Это дискриминант так реши

Answer 2

Graph of the Function y = x^2 + 2x - 6

To graph the function y = x^2 + 2x - 6, we can plot several points and connect them to form a smooth 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 = x^2 + 2x - 6

Using the quadratic formula, we can find the x-values: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 2, and c = -6. Plugging these values into the quadratic formula, we get: x = (-2 ± √(2^2 - 4(1)(-6))) / (2(1)) x = (-2 ± √(4 + 24)) / 2 x = (-2 ± √28) / 2 x = (-2 ± 2√7) / 2 x = -1 ± √7

So the x-intercepts are approximately x = -1 + √7 and x = -1 - √7.

To find the y-intercept, we set x = 0 and solve for y: y = (0)^2 + 2(0) - 6 y = -6

So the y-intercept is y = -6.

We can also find additional points by substituting different x-values into the equation. For example, when x = 1, we have: y = (1)^2 + 2(1) - 6 y = -3

When x = 2, we have: y = (2)^2 + 2(2) - 6 y = 2

Using these points, we can plot the graph of the function y = x^2 + 2x - 6.