What are the x- and y-intercepts of the graph of y = x2 + x - 6?
Solution:
The x-intercepts of the curve can be determined by putting y = 0 and the y-intercepts can be determined by putting x = 0.
a) Determination of x-intercepts
When we are determining the x-intercepts of the given function we are determining the zeroes of the function.
These are the values of x for which the y value will be zero. Therefore we have
x2 + x - 6 = 0
Factorising the quadratic equation by splitting the middle term, we get
x2 + 3x - 2x - 6 = 0
x(x + 3) - 2(x + 3) = 0
(x - 2)(x + 3) = 0
Hence, x = 2 , -3 are the values of x-intercept.
b) Determination of y-intercept
The y-intercept can be determined when x = 0. Therefore
y = (0)2 + 1(0) - 6 = -6
Therefore, the value of the y-intercept is y = -6.
The x-intercept and y-intercepts are depicted in the graph below:
What are the x- and y-intercepts of the graph of y = x2 + x - 6?
Summary:
The x- and y-intercepts of the graph of y = x2 + x - 6 are x = 2, x = -3 and y = -6.