Label exact values for all x and y intercepts.
Q1:
f(x)=x^3-2x^2-5x+10
f(x)=X^2(x-2)-5(x-2)
f(x)=(x-2)(x^2-5)
f(x)=(x-2)(???)
Q2:
f(x)=x^4-5x^2
f(x)=x^2(x^2-5)
f(x)=???
please help and thank you
1) (x-2)(x-sqrt5)(x+sqrt5)
2) same thinking.
what about x^2 in Q2? I'm suppose to graph this. So the x-int is 0? so does that mean the line won't pass through that point?
To find the x-intercepts of a function, we need to determine the values of x where the function intersects or crosses the x-axis. In other words, these are the points where the value of y (or f(x)) is equal to zero.
Q1:
To find the x-intercepts of the function f(x) = (x-2)(x^2-5), we set f(x) equal to zero and solve for x:
0 = (x-2)(x^2-5)
Since the product of two factors is zero, one or both of the factors must be equal to zero. Therefore, we set each factor equal to zero and solve for x:
x - 2 = 0 or x^2 - 5 = 0
Solving each equation separately:
x - 2 = 0 => x = 2
For the second equation, x^2 - 5 = 0, we can rearrange it as:
x^2 = 5
Taking the square root on both sides:
x = ±√5
So, the x-intercepts are: x = 2 and x = ±√5.
To find the y-intercept, we need to determine the value of y when x is equal to zero. So, we substitute x = 0 into the function and evaluate:
f(0) = (0-2)(0^2-5)
f(0) = -2(0-5)
f(0) = -2(-5)
f(0) = 10
Therefore, the y-intercept is (0, 10).
In summary, the x-intercepts for f(x) = (x-2)(x^2-5) are x = 2 and x = ±√5, and the y-intercept is (0, 10).
Q2:
To find the x-intercepts of the function f(x) = x^2(x^2-5), we set f(x) equal to zero and solve for x:
0 = x^2(x^2-5)
Since the product of two factors is zero, one or both of the factors must be equal to zero. Therefore, we set each factor equal to zero and solve for x:
Either x^2 = 0 or x^2 - 5 = 0
For the first equation, x^2 = 0, we obtain x = 0.
For the second equation, x^2 - 5 = 0, we can rearrange it as:
x^2 = 5
Taking the square root on both sides:
x = ±√5
So, the x-intercepts are: x = 0 and x = ±√5.
Since the function f(x) = x^2(x^2-5) does not include any linear term (ax or bx), there is no y-intercept for this function.
In summary, the x-intercepts for f(x) = x^2(x^2-5) are x = 0 and x = ±√5, and there is no y-intercept for this function.