What are the x- and y-intercepts of the graph of y = x2 + 7x + 12?
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 + 7x + 12 = 0
Factorising the left hand side we get,
⇒ x2 + 4x + 3x + 12 = 0
⇒ x(x + 4) + 3(x + 4) = 0
⇒ (x + 4)(x + 3) = 0
Therefore,
x + 4 = 0 ⇒ x = -4, The first x-intercept
x + 3 = 0 ⇒ x = -3, The second x - intercept
b) Determination of y - intercept
The y-intercept can be determined when x = 0. Therefore
y = (0)⇒ + 7(0) + 12 = 12
Therefore the y-intercept is 12.
The x - intercepts and y-intercept are depicted in the graph below:
What are the x- and y-intercepts of the graph of y = x2 + 7x + 12?
Summary:
The x- and y-intercepts of the graph of y = x2 + 7x + 12 are -3, -4 and 12 respectively.