To graph equations like y = -x -12
Since this is in slope intercept form we are automatically given the y-intercept which in this case is -12 so (0,-12)
the coefficient in front of the x is the slope, in this case it is -x so that means -1/1 or -1
To graph this you would plot a point at the y-intercept, then down one over one (negative slope means down instead of up) then to the right, however long to create a line
Hope this helps :)<span />
Answer:
Please see the attachment.
Step-by-step explanation:
![\text{Given function:}f(x)=-x^3+4x^2-x+3](https://tex.z-dn.net/?f=%5Ctext%7BGiven%20function%3A%7Df%28x%29%3D-x%5E3%2B4x%5E2-x%2B3)
Now we find the x and y intercept of f(x)
For x-intercept: Put f(x)=0 and solve for x
So, x=3.92 (Just before 4 on x-axis)
For y-intercept: Put x=0 and solve for f(0)
So, y=3 (Passes through y-axis at 3)
End Behavior: Third degree function
![x\rightarrow -\infty , f(x)\rightarrow \infty](https://tex.z-dn.net/?f=%20x%5Crightarrow%20-%5Cinfty%20%2C%20f%28x%29%5Crightarrow%20%5Cinfty)
![x\rightarrow \infty , f(x)\rightarrow -\infty](https://tex.z-dn.net/?f=%20x%5Crightarrow%20%5Cinfty%20%2C%20f%28x%29%5Crightarrow%20-%5Cinfty)
Possible graph of the f(x). Please see the attachment.
Answer:
x^3-x^2+x-2+x^4
Step-by-step explanation:
Remove parenthesis.
3x^3-4x^2+x-7+x^4-2x^3+3x^2+5
Collect like terms.
(3x^3-2x^3)+(-4x^2+3x^2)+x+(-7+5)+x^4
Simplify.
x^3-x^2+x-2+x^4
The equation of the parabola is y = 5x² - 11x - 31
<h3>Parabola</h3>
The equation of a parabola is a quadratic equation in the form:
y = ax² + bx + c
Where a, b and c are constants.
At point (2, - 33):
- -33 = a(2)² + b(2) + c
- 4a + 2b + c = -33 (1)
At point (4, 5):
- 5 = a(4)² + b(4) + c
- 16a + 4b + c = 5 (2)
At point (5, 39):
- 39 = a(5)² + b(5) + c
- 25a + 5b + c = 39 (3)
Solving equation 1, 2 and 3 simultaneously gives:
a = 5, b = -11, c = -31.
The equation of the parabola is y = 5x² - 11x - 31
Find out more on parabola at: brainly.com/question/4148030