Answer:
y intercept = -2
x intercepts = -2,-1,1
Step-by-step explanation:
f(x) = x^3 + 2x^2 -x-2
Set this equation equal to zero to find the x intercepts.
Factoring by grouping
0 =x^3 -x +2x^2 -2
= x( x^2-1) +2(x^2-1)
Factoring out the (x^2-1)
0= (x^2-1) (x+2)
Factoring the first term using the difference of squares (a^2-b^2) = (a-b)(a+b)
0 = (x-1) (x+1) (x+2)
Using the zero product property
x-1 = 0 x+1 = 0 x+2 =0
x=1, x=-1 x=-2
The x intercepts are -2, -1, 1
To find the y intercepts, set x=0
y = x^3 + 2x^2 -x-2
y = 0 -2
y = -2
Answer:
10 units
Step-by-step explanation:
Using the distance formula above,
distance between the 2 points
![= \sqrt{[0 - ( - 8)]^{2} + (7 - 1)^{2} } \\ = \sqrt{(0 + 8)^{2} + 6^{2} } \\ = \sqrt{ {8}^{2} + 36} \\ = \sqrt{64 + 36} \\ = \sqrt{100} \\ = 10 \: units](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B%5B0%20-%20%28%20-%20%208%29%5D%5E%7B2%7D%20%2B%20%287%20-%201%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%280%20%2B%208%29%5E%7B2%7D%20%2B%206%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%7B8%7D%5E%7B2%7D%20%20%2B%2036%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B64%20%2B%2036%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B100%7D%20%20%5C%5C%20%20%3D%2010%20%5C%3A%20units)
Answer:
B
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - 
y = 3x² + 6x + 1 ← is in standard form
with a = 3 and b = 6 , then
= - 
= - 1
Substitute x = - 1 into y for corresponding y- coordinate
y = 3(- 1)² + 6(- 1) + 1
= 3(1) - 6 + 1
= 3 - 5
= - 2
vertex = (- 1, - 2 )
Answer:
(40 + 2x)feet
Step-by-step explanation:
see attachment for the figure.
Let 'L' represents the length of the rectangular swimming pool i.e 40ft wide.
and pool is bordered by square tiles that are x feet in length surrounding the pool
therefore,
In order to find the longest side of the pool and the tile border, take the sum of length of the swimming pool i.e 40 adding two times the wide of the square tiles
(40+2x)feet.
