What are the x-intercept and y-intercept of the graph of y = x2 + x − 6?
We will use the concept of a quadratic equation to find the x-intercept and y-intercept.
Answer: For the given graph y = x2 + x − 6, the y-intercept = - 6 and the x-intercept = 2, -3.
Let us see how will we use the concept of a quadratic equation to find the x-intercept and the y-intercept.
Given: y = x2 + x − 6
The y-intercept is the point where the curve cuts the y-axis and the coordinates of the x-axis at that point is 0.
Hence, substituting x = 0 in the given equation y = x2 + x − 6 we get,
y = 0 + 0 - 6
⇒ y = -6
Hence, the value of the y-intercept is y = -6.
Similarly, the x-intercept is the point where the graph cuts the x-axis and the coordinates of the y-axis at that point is 0.
Hence, substituting y = 0 in the equation we get x2 + x − 6 = 0 we get,
x2 + x - 6 = 0
⇒ x2 + 3x - 2x - 6 = 0 [By splitting the middle term]
⇒ x (x + 3) - 2 (x + 3) = 0
⇒ (x - 2) (x + 3) = 0
Hence, x = 2 , -3 are the values of x-intercept.