For each parabola, you have to do a system of equation with the line y = x - 5 and find which of them has one real solution.
For that you can solve the systems and find the roots, but you can also use the rule that to have one real solution the discriminant of the quadratiic equation (b^2 - 4ac) has to be zero.
1)
y = x - 5
y = x^2 + x - 4
=> x - 5 = x^2 + x - 4
=> x^2 + 1 = 0
It is easy to tell, by simple inspection, that this equation has not real solutions.
2)
y = x -5
y = x^2 + 2x - 1
=> x - 5 = x^2 + 2x - 1
=> x^2 + x + 4 = 0
discriminant = b^2 - 4ac = 1^2 - 4(1)(4) = 1 - 16 = - 15
A negative discriminant means that there are not real solutions.
3)
y = x - 5
y = x^2 + 6x + 9
x - 5 = x^2 + 6x + 9
=> x^2 + 5x + 14 = 0
=> b^2 - 4ac = 5^2 - 4(1)(14) = 25 - 56 = - 31 => no real solutions
4)
y = x - 5
y = x^2 + 7x + 4
x - 5 = x^2 + 7x + 4
=> x^2 + 6x + 9 = 0
=> b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0 => the system has one real solution.
By the way, that solution is easy to find because you can factor the equation as: (x + 3)^2 = 0 => x = - 3
Ok
y=mx+b
b=yintercept
that's all you need to know
ok so we just list the yintercepts then order them
10,0.5,3,-5,7,-12
arrange from least to greatest
-12,-5,0.5,37,10
so the order of the functions is
y=-5x-12
y=0.5x-5
y=-4.5+3
y=-2x+7
y=2.5x+10
Answer:
45 is 125% of 36, and 36 is 80% of 45.
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation: