Plot the graph of p(x)=X^2± X-12 and find its zeros
Answers
Explanation:
To plot the graph of the quadratic equation p(x) = x^2 + x - 12, we first need to find the zeros or roots of the equation, which are the x-coordinates of the points where the graph of the equation intersects the x-axis.
The zeros of the equation can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 1, and c = -12.
Plugging in the values, we get:
x = (-1 ± √(1^2 - 4 * 1 * -12)) / 2 * 1
x = (-1 ± √(1 + 48)) / 2
x = (-1 ± 7) / 2
So, the zeros of the equation are x = (-1 + 7) / 2 = 3 and x = (-1 - 7) / 2 = -4.
These zeros divide the x-axis into three sections, two of which correspond to the two branches of the parabola that opens upward. The third section corresponds to the x-interval in which the graph of the equation lies below the x-axis.
So, we can plot the graph by first plotting the zeros on the x-axis and then plotting the points on the graph that correspond to a few x-values. By connecting these points, we can see the shape of the graph.