Answer:
Can you give me the choices for each of these, I'm not sure how they might phrase it.
Answer:
vertex = (- 1, 1 )
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 = x² + 2x + 2 ← is in standard form
with a = 1 and b = 2 , then
x = - 
= - 1
substitute x = - 1 into the equation for y- coordinate of vertex
y = (- 1)² + 2(- 1) + 2 = 1 - 2 + 2 = 1
vertex = (- 1, 1 )
Since anything multiplied by zero produces zero, we can say 0(a + 1) = 0 and (2a - 2)(0) = 0.
Thus, 2a - 2 = 0 or a + 1 = 0
2a = 2
a = 1
a = -1
We can conclude that a = 1 or - 1 will produce the end result as 0.
Answer: The two integers are 8 and 9.
Step-by-step explanation: Let n represent the number.
n^2 + (n + 1)^2 = 145
By foiling, this can be rearranged to:
n^2 + n^2 + 2n + 1 = 145
Subtract 145 from both sides:
2n^2 + 2n - 144 = 0
Divide both sides by 2:
n^2 + n - 72 = 0
Factor the polynomial:
(n + 9)(n - 8) = 0
Solve for n:
n = -9, n = 8
Since they need to be consecutive, make the 9 positive. It will be positive either way because it is being squared.
Now, n = 9 and n = 8.
These are your two integers. Hope this helps!
Answer:
Hi! Sorry this is coming a bit late, But your answer is B: formula for the slope of a line, D: problem solving by solving simpler parts first, and E: Cartesian plane for graphing. I hope this helps in any way! ^_^
Step-by-step explanation:
