Answer:
Step-by-step explanation:
Please use " ^ " to indicate exponentation: y= x^2 + 11x + 24. Thanks.
Because x^2 is positive, the graph of this parabola opens up.
We can find the vertex and roots (zeros) as follows, using the quadratic formula:
With a = 1, b = 11 and c = 24,
-11 ± √ [ (11^2-4(1)(24) ] -11 ± √25
x = ------------------------------------ = --------------- = -3 and x = -8
2(1) 2
This tells us that the x-intercepts are at (-3, 0) and (-8, 0). The minimum value is at x = -b / (2a), which here is x = -11 / [2] = -5 1/2 (which is halfway between the zeros).
The vertex (and thus, the minimum) is at (-5 1/2, f(-5 1/2) ).
Answer:
P(x) = - 5(x + 2)²(x - 3)
Step-by-step explanation:
Given roots x = - 2 with multiplicity 2 and x = 3 , then the factors are
(x + 2)² and (x - 3)
P(x) is then the product of the factors, that is
P(x) = a(x + 2)²(x - 3) ← a is a multiplier
To find a substitute (2, 80) into P(x)
80 = a(2 + 2)²(2 - 3) = a(16)(- 1) = - 16a ( divide both sides by - 16 )
a = - 5
P(x) = - 5(x + 2)²(x - 3)
Answer:
z = 66
Step-by-step explanation:
RS = z
QT = z - 33
Based on the midsegment theorem, QT = ½(RS)
Plug in the values
z - 33 = ½(z)
Multiply both sides by 2
2(z - 33) = z
2z - 66 = z
Add 66 to both sides
2z = z + 66
Subtract z from both sides
2z - z = 66
z = 66
