Find the x-intercept and y-intercept (zeroes of the function)
1.) P(x)=x^4- 9x^2
2.) P(x)= 2(x-5)(x+2)^2
#1.
P(x) = x^2(x^2-9) = x^2(x-3)(x+3)
x-intercepts are clearly 0,-3,3
P(0) = 0 for the y-intercept.
thanks a lot... :)
To find the x-intercept and y-intercept (zeroes of the function), we set the given function equal to zero and solve for the corresponding values.
For the first function, P(x) = x^4 - 9x^2:
1.) X-intercept (Zeroes):
To find the x-intercept, we set P(x) equal to zero and solve for x:
x^4 - 9x^2 = 0
Factor out common terms:
x^2(x^2 - 9) = 0
Set each factor equal to zero and solve for x:
1) x^2 = 0
x = 0
2) x^2 - 9 = 0
(x - 3)(x + 3) = 0
Solve for x in each factor:
x - 3 = 0 --> x = 3
x + 3 = 0 --> x = -3
Therefore, the x-intercepts (zeroes) of the function P(x) = x^4 - 9x^2 are x = 0, x = 3, and x = -3.
2.) Y-intercept:
To find the y-intercept, we set x equal to 0 and evaluate P(x):
P(0) = 0^4 - 9(0^2)
P(0) = 0
Therefore, the y-intercept of the function P(x) = x^4 - 9x^2 is at the point (0, 0).
For the second function, P(x) = 2(x - 5)(x + 2)^2:
1.) X-intercept (Zeroes):
To find the x-intercepts, we set P(x) equal to zero and solve for x:
2(x - 5)(x + 2)^2 = 0
Set each factor equal to zero and solve for x:
1) x - 5 = 0 --> x = 5
2) (x + 2)^2 = 0
x + 2 = 0 --> x = -2
Therefore, the x-intercepts (zeroes) of the function P(x) = 2(x - 5)(x + 2)^2 are x = 5 and x = -2.
2.) Y-intercept:
To find the y-intercept, we set x equal to 0 and evaluate P(x):
P(0) = 2(0 - 5)(0 + 2)^2
P(0) = 2(-5)(2)^2
P(0) = 2(-5)(4)
P(0) = -40
Therefore, the y-intercept of the function P(x) = 2(x - 5)(x + 2)^2 is at the point (0, -40).