x and y intercept of y=x^3+7x^2+10x
for the x-intercept let y = 0
x^3 + 7x^2 + 10x = 0
x(x^2 + 7x + 10) = 0
x(x+2)(x+5) = 0
so x = 0, -2, -5
(your x-intercepts)
for the y-intercept, let x = 0
then of course y=0
so 3 x-intercepts, one y-intercept
To find the x-intercept of the equation y = x^3 + 7x^2 + 10x, we set y to 0 and solve for x.
0 = x^3 + 7x^2 + 10x
Next, we can factor out an x from the equation:
0 = x(x^2 + 7x + 10)
Now, we need to solve the quadratic equation x^2 + 7x + 10 = 0. This can be factored as:
0 = (x + 2)(x + 5)
Setting each factor equal to 0, we get:
x + 2 = 0 or x + 5 = 0
Solving for x, we find:
x = -2 or x = -5
Therefore, the x-intercepts of the equation y = x^3 + 7x^2 + 10x are -2 and -5.
To find the y-intercept, we set x to 0 and solve for y.
y = (0)^3 + 7(0)^2 + 10(0)
y = 0
Therefore, the y-intercept of the equation y = x^3 + 7x^2 + 10x is 0.
To find the x-intercept of a function, we set y equal to zero and solve for x. This gives us the values of x where the function intersects or crosses the x-axis.
In this case, the given function is y = x^3 + 7x^2 + 10x. Setting y = 0, we have:
0 = x^3 + 7x^2 + 10x
To solve this equation, we can factor out an x from the right side:
0 = x(x^2 + 7x + 10)
Now, we have two possibilities:
1. x = 0: This is one possible x-intercept. When x = 0, the function crosses the x-axis at the origin (0,0).
2. x^2 + 7x + 10 = 0: To find the other x-intercepts, we need to solve this quadratic equation. We can either factor it or use the quadratic formula:
Factoring:
0 = (x + 5)(x + 2)
Setting each factor equal to zero:
x + 5 = 0 or x + 2 = 0
Solving for x, we find:
x = -5 or x = -2
So, the x-intercepts of the given function are x = 0, x = -5, and x = -2.
To find the y-intercept of a function, we set x equal to zero and solve for y. This gives us the value of y where the function intersects or crosses the y-axis.
In this case, the given function is y = x^3 + 7x^2 + 10x. Setting x = 0, we have:
y = 0^3 + 7(0^2) + 10(0)
Simplifying this expression, we get:
y = 0
So, the y-intercept of the given function is y = 0. The function intersects the y-axis at the point (0,0).